First, grab the precompiled binary file (memcache.so) from here. There were no problems using this on Snow Leopard (for me, at least).
Second, copy the file to your MAMP extensions directory. You should be able to find it here: /Applications/MAMP/bin/php5/lib/php/extensions/no-debug-non-zts-[date].
Find the extensions section (about line 540 or so) and add this line to the list of extensions:
Once that’s done, save php.ini and reboot MAMP. You should be able to see an entry for memcache when opening your phpinfo page.