Put the SoD patcher somewhere you can access it easily - it should be your launcher for the game. Personally, I shove it into my game directory and create a shortcut to it there. Not necessary though, just a suggestion - you can run the SoD patcher from anywhere you want! If you're running in Windows Vista or 7, you may need to give the program permission to access your computer.
In the patcher window, click [Browse] and select the game directory.
Hit [Patch and Run] and wait for a while. The patcher downloads Mumble first (it takes forever for me!), EQW and updates the files in your game directory. The patcher window has a lot of little buttons and boxes, but leave them be for now.
As soon as patching finishes the patcher itself will close a window for EQW will pop open. Click the [Browse] button in this window as well, find the game directory again, and select eqgame.exe. Again, leave the little checkboxes alone - shouldn't ever even need to consider changing these. Only Fix eqclient.ini should be checked.
From here, you can click Start EQ and the game client should open to the EULA.