If you don't want to deal with the EQEmuLauncher, here's how you update your files manually:
There'll be a link to the latest eqchanges zip on the front page. It's up to V14 now and the
link leads directly to the download. Extract that zip directly into your Everquest directory and agree to all the file overrides. That's all.
If you get an error when you try to run the game afterwards, that's because the latest patch has screwed something up for many of us. Look
here or
here for possible fixes. Unfortunately, some of us haven't had any luck with those fixes yet, so hopefully someone comes up with something soon.