If you are downloading the 52MB file named directx_apr2006_redist.exe, it is a self extracting compressed file. You can download it to whichever directory you want.
When it is executed, it attempts to extract (unzip, if you prefer) the DirectX install files and asks you where to put them. You can put these wherever you want. I recommend creating a new temporary directory named DX or something similar right on your desktop or in your My Documents folder, but wherever is convenient is fine, and telling the program to place the install files in this new directory.
Then you must display the files inside the directory (with My Computer, Windows Explorer, or what utility you prefer to use to display files on your hard drive) and run (double-click) the file named DXSetup.exe. I think that is the correct name. It is the only .exe file in the whole directory. If your file extensions are hidden, it should be the only file of type Application, I think.
This will start the actual DirectX update process. There are a few dialog boxes to go through first including the license agreement, etc., and then eventually you should see a progress bar with a message telling you that it is searching for files to update (or something like that). You may or may not have to reboot afterwards. It depends on your OS, I think.
After all this, you should be able to run the DirectXTest.exe program in your Everquest directory and after several seconds receive a little window that says you are all set.
I think this is all accurate, but I am writing this from memory, so if yours appears slightly different, it is probably a mistake on my part.
Alternate update methods:
If you are downloading the file named dxwebsetup.exe, I believe you can also save it wherever you want, then run it to complete the update, although I did not do it this way, so I don't have details.
I believe you can also just Run the file dxwebsetup.exe from the website instead of downloading it, but I have not done that either.
I hope this helps.
Edited, Jun 13th 2006 at 1:32pm EST by Steale