Ben Goodger says in this thread:
Extension-Manager enabled builds should be available today on ftp.m.o [ftp.mozilla.org]. Please start using these and test the new EM, file bugs!
"Today" being 24 May of course. The Extension Manager is partially functional now in branch builds (which you can get from the Mozilla Firefox nightly FTP site - just look for dates ending with "-0.9"). Get one of these builds, either 2004-05-24-0.9 build or the very fresh 2004-05-25-10-0.9 build (of course, if there are later builds by the time you read this, you should get those instead).
Only extensions that have been updated to work with the new Extensions API will be reflected in the Extension Manager (other extensions should install fine, but they won't be listed in the Extension Manager - they appear in Tools -> Options -> Themes as before). I tried out Content Holder and ContextMenu Extensions just to see how they work.
Turns out they install just fine in a download manager-like kind of way. And after a restart of Firefox, they show up just fine.
The "Checking for Updates" for extensions doesn't work correctly yet - it shows a "New Updates Available" notification whether or not there actually are any new updates.