DVDX is a homebrew application that installs a hidden "channel" which can be used by other homebrew applications to access home burned and factory pressed DVD content without the need for a modchip. This does not modify any IOS in any way, making it very safe.
There are a few different installers for DVDX. You should read carefully and chose the one that best suits you.
For System Menus 3.2 and 3.3
This should be the preferred installer for most users since it has some special options not found in any of the other installers. You will need this if you are using MPlayer_CE and want the USB 2.0 speed capability to be properly detected, or if you have a mod chip. If you do have a mod chip, you may need to install PatchMii core before installing DVDX. Then, when asked for the installation mode, select PatchMii.
For System Menu 3.4
You will probably not want to use this installer, as it has essentially been made redundant by the Hackmii installer. But if you just want to use a simple DVDX installer and you have System Menu 3.4, you can use this. This installer version does not have the PatchMii and advanced modes. That means that some modchip users cannot install it. Please remember that it will need an internet connection to work.
For all System Menus up to and including 4.1
Q: What type of DVD should I use?
A: Pressed DVD-ROM video discs of course work. For recordables, DVD-R media is recommended. However, DVDX has been confirmed working with various DVD media, including DVD+R/RW and DVD-R/RW discs. Particular brands (lower quality discs) may be problematic, and different Wii drives have different levels of compatibility. Please note that DVD+R/RW discs will need to have their BookType set to DVD-ROM to work properly in Normal mode (if you have no modchip). PatchMii mode does not have this requirement, but requires a modchip.
Q: Why does my Wii not read my DVDs?
A: Be sure that you properly install DVDX, and that the application that you are trying to use supports it. If you are using a burned disc, make sure it is burned correctly. Try re-burning the DVD on a DVD-R if it is not already. If you are using one of Tantric's apps (the GX emulators), try using an older version, as many times in the past he has accidently broken DVD support.
Homebrew developers looking to add DVD support to their applications will need to use libdi, which has been added to libogc. libdi requires the DVDX stub.