Basics
The Wii is this generation's system to hack because of all its vulnerabilities without the need for extra hardware, and there's a lot of fun to be had in the homebrew scene for the Wii. So where to start?
I want to begin this by noting that hacking the Wii isn't quite straight-forward because as vulnerabilities are exploited, Nintendo patches them through updates so they will no longer be vulnerable. Each time one thing is patched, there is another exploit. So bear with me as I try to go over the different exploits available depending on the system menu version you are working with.
Exploits
Twilight Hack (System Menu <4.0)
Let's start with the original exploit; the Twilight Hack. For the Twilight Hack, you will need a copy of Twilight Princess for the Wii, the Gamecube version will not work. You will need a hacked Twilight Princess save file. You will need an SD card (note: SDHC will not work with this). On the SD card, you will have the homebrew application you wish to run through the hack. For system menu 3.3 and earlier, Twilight Hack v-0.1 beta-1 will do the trick. For System menu 3.4, Twilight Hack v-0.1 beta-2 will be what you need. You can download them here: http://hbc.hackmii.com/download/ . For more information on the twilight hack, go to the Wiibrew wiki: http://wiibrew.org/wiki/Twilight_Hack .
Bannerbomb (System Menu <4.3)
If your Wii has been updated to System Menu 4.0, however, it appears that the Twilight Hack has been put to rest for good. Fortunately, another vulnerability has been discovered and it is called the Bannerbomb. You will need the Bannerbomb http://bannerbomb.qoid.us/ . You will need an SD card (SDHC will work if you have system menu 4.0). I have not personally done this hack, so here's a link that will probably help better than I can: http://wiibrew.org/wiki/Bannerbomb. Bannerbomb has since been fixed as of System Menu 4.2. Bannerbomb v2 now works with System Menu 4.2, but does not work with 4.3.
SmashStack & IndianaPwns (All Current System Menus)
There is another hack that has been discovered called the SmashStack. It requires a copy of Super Smash Brothers Brawl. From what I've read, it will need a file to be copied over your Custom Levels file or something. http://wiibrew.org/wiki/Smash_Stack
Another new hack released by TeamTwiizers, responsible for the Twilight hack, called IndianaPwns. This involves a hacked Lego Indiana Jones game file. For more details, http://wiibrew.org/wiki/Indiana_Pwns
Both the SmashStack and IndianaPwns are still functional as of System Menu 4.2.
Applications
Those exploits just lift the lid off of Pandora's box. What you'll want to do using these exploits is to install something called the Homebrew Channel, which is a Channel that will show up in your Wii System Menu. When you launch the channel, you will be taken to a menu with all the homebrew applications you have stored on your SD card, and you can launch them from there with minimal hassle.
DVDx is a program that allows your homebrew applications to read DVDs. With it you will be able to watch DVD movies or load files from a DVD.
Bootmii: Bootmii is a program that loads up before the Wii System Menu does. It allows you to boot directly into the Homebrew Channel if you so please. One of the complaints about the Wii is that you can't control the system menu with a gamecube controller, but Bootmii is controllable with a gamecube controller (but not a Wii controller). You can use it to boot gamecube games without touching a Wii controller if you boot directly into the Homebrew channel and run a homebrew application called gcloader, which will boot gamecube discs. Note: Not all games will boot with GCloader, there is a compatibility list, but its far from comprehensive. Gecko OS, which is described more extensively later in this post. Now I mentioned that the Wii controller is not compatible with Bootmii, so I'm sure someone is thinking that it then becomes a hassel having to pick up a gamecube controller to get into the System Menu to start a Wii game, but that is not the case. You can edit the Bootmii .ini file so that it automatically boots to the system menu or homebrew channel after a delay of your choosing. I personally set mine to boot the homebrew channel since you can directly boot discs or homebrew apps from there or easily go to the system menu if you really need to regardless of the controller in your hand.
Installing the Homebrew Channel, DVDx, and Bootmii: Well, its as simple as executing either the Twilight hack or the Bannerbomb. Where you would place the homebrew application you wish to run with the hack, you put the Homebrew Channel installer, which is now bundled with the Hackmii installer http://bootmii.org/download/ . The Hackmii installer will go through and check your system to see if you are capable of installing the Homebrew Channel, DVDx, and Bootmii. Select the option to install the homebrew channel and it will install it. At this point in time, you may choose to install DVDx and Bootmii.
Other things of interest
Homebrew Browser: The Homebrew Browser is a Homebrew application you can install into the Homebrew Channel that allows you to browse, download, and install homebrew applications straight off of the internet. No need to swap out your SD card to you PC and back to your Wii in order to install an application anymore because of this useful program.
Gecko OS: Gecko OS allows you to boot Wii and gamecube disks from the homebrew channel. It also includes features such as region-free, loading SD Cheats and File Patches. So aside from being able to boot disks without ever needing to go into the main wii menu (if used in conjunction with BootMii), you can play japan-only games. Fatal Frame IV, for example, will not get a US release, but it will run through region free, and through the SD File patcher, you'll be able to run it with an English translation that is currently being worked on.
GCLoader: GCLoader is a homebrew app that will launch Gamecube disks. Used in conjunction with Bootmii and the homebrew channel, it is possible to boot gamecube games with only the use of your gamecube controller instead of needing to use a wii controller to select the disk channel. There are some compatibility issues with this app, and some games will crash, especially when accessing the memory card. This program doesn't seem to be very useful anymore since Gecko OS boots both Wii and GCN games without really any problems.
Any further curiosity into the hacking of the Wii, just browse look around the Wiibrew Wiki: http://wiibrew.org/wiki/Main_Page
The Wii is this generation's system to hack because of all its vulnerabilities without the need for extra hardware, and there's a lot of fun to be had in the homebrew scene for the Wii. So where to start?
I want to begin this by noting that hacking the Wii isn't quite straight-forward because as vulnerabilities are exploited, Nintendo patches them through updates so they will no longer be vulnerable. Each time one thing is patched, there is another exploit. So bear with me as I try to go over the different exploits available depending on the system menu version you are working with.
Exploits
Twilight Hack (System Menu <4.0)
Let's start with the original exploit; the Twilight Hack. For the Twilight Hack, you will need a copy of Twilight Princess for the Wii, the Gamecube version will not work. You will need a hacked Twilight Princess save file. You will need an SD card (note: SDHC will not work with this). On the SD card, you will have the homebrew application you wish to run through the hack. For system menu 3.3 and earlier, Twilight Hack v-0.1 beta-1 will do the trick. For System menu 3.4, Twilight Hack v-0.1 beta-2 will be what you need. You can download them here: http://hbc.hackmii.com/download/ . For more information on the twilight hack, go to the Wiibrew wiki: http://wiibrew.org/wiki/Twilight_Hack .
Bannerbomb (System Menu <4.3)
If your Wii has been updated to System Menu 4.0, however, it appears that the Twilight Hack has been put to rest for good. Fortunately, another vulnerability has been discovered and it is called the Bannerbomb. You will need the Bannerbomb http://bannerbomb.qoid.us/ . You will need an SD card (SDHC will work if you have system menu 4.0). I have not personally done this hack, so here's a link that will probably help better than I can: http://wiibrew.org/wiki/Bannerbomb. Bannerbomb has since been fixed as of System Menu 4.2. Bannerbomb v2 now works with System Menu 4.2, but does not work with 4.3.
SmashStack & IndianaPwns (All Current System Menus)
There is another hack that has been discovered called the SmashStack. It requires a copy of Super Smash Brothers Brawl. From what I've read, it will need a file to be copied over your Custom Levels file or something. http://wiibrew.org/wiki/Smash_Stack
Another new hack released by TeamTwiizers, responsible for the Twilight hack, called IndianaPwns. This involves a hacked Lego Indiana Jones game file. For more details, http://wiibrew.org/wiki/Indiana_Pwns
Both the SmashStack and IndianaPwns are still functional as of System Menu 4.2.
Applications
Those exploits just lift the lid off of Pandora's box. What you'll want to do using these exploits is to install something called the Homebrew Channel, which is a Channel that will show up in your Wii System Menu. When you launch the channel, you will be taken to a menu with all the homebrew applications you have stored on your SD card, and you can launch them from there with minimal hassle.
DVDx is a program that allows your homebrew applications to read DVDs. With it you will be able to watch DVD movies or load files from a DVD.
Bootmii: Bootmii is a program that loads up before the Wii System Menu does. It allows you to boot directly into the Homebrew Channel if you so please. One of the complaints about the Wii is that you can't control the system menu with a gamecube controller, but Bootmii is controllable with a gamecube controller (but not a Wii controller). You can use it to boot gamecube games without touching a Wii controller if you boot directly into the Homebrew channel and run a homebrew application called gcloader, which will boot gamecube discs. Note: Not all games will boot with GCloader, there is a compatibility list, but its far from comprehensive. Gecko OS, which is described more extensively later in this post. Now I mentioned that the Wii controller is not compatible with Bootmii, so I'm sure someone is thinking that it then becomes a hassel having to pick up a gamecube controller to get into the System Menu to start a Wii game, but that is not the case. You can edit the Bootmii .ini file so that it automatically boots to the system menu or homebrew channel after a delay of your choosing. I personally set mine to boot the homebrew channel since you can directly boot discs or homebrew apps from there or easily go to the system menu if you really need to regardless of the controller in your hand.
Installing the Homebrew Channel, DVDx, and Bootmii: Well, its as simple as executing either the Twilight hack or the Bannerbomb. Where you would place the homebrew application you wish to run with the hack, you put the Homebrew Channel installer, which is now bundled with the Hackmii installer http://bootmii.org/download/ . The Hackmii installer will go through and check your system to see if you are capable of installing the Homebrew Channel, DVDx, and Bootmii. Select the option to install the homebrew channel and it will install it. At this point in time, you may choose to install DVDx and Bootmii.
Other things of interest
Homebrew Browser: The Homebrew Browser is a Homebrew application you can install into the Homebrew Channel that allows you to browse, download, and install homebrew applications straight off of the internet. No need to swap out your SD card to you PC and back to your Wii in order to install an application anymore because of this useful program.
Gecko OS: Gecko OS allows you to boot Wii and gamecube disks from the homebrew channel. It also includes features such as region-free, loading SD Cheats and File Patches. So aside from being able to boot disks without ever needing to go into the main wii menu (if used in conjunction with BootMii), you can play japan-only games. Fatal Frame IV, for example, will not get a US release, but it will run through region free, and through the SD File patcher, you'll be able to run it with an English translation that is currently being worked on.
GCLoader: GCLoader is a homebrew app that will launch Gamecube disks. Used in conjunction with Bootmii and the homebrew channel, it is possible to boot gamecube games with only the use of your gamecube controller instead of needing to use a wii controller to select the disk channel. There are some compatibility issues with this app, and some games will crash, especially when accessing the memory card. This program doesn't seem to be very useful anymore since Gecko OS boots both Wii and GCN games without really any problems.
Any further curiosity into the hacking of the Wii, just browse look around the Wiibrew Wiki: http://wiibrew.org/wiki/Main_Page
I'm like win there 
