When you installed it, it put a file named homebrew.mxcl.memcached.plist in /usr/local/Cellar/memcached/$version/; you copy that file into ~/Library/LaunchAgents and then tell launchd to start it with launchctl load -w ~/Library/LaunchAgents/homebrew.mxcl.memcached.plist.
If you were watching the console carefully during the brew install command, it should have said something about doing these exact steps. If you run brew info it'll re-print this information, e.g. brew info memcached.
You should probably read https://docs.brew.sh/Manpage -- it has more useful documentation including the brew remove command which will remove the package if you decide you don't want it.
Additionally you can run "brew info", if you have forgotten about the instructions.
→ brew info memcached
memcached 1.4.7
http://memcached.org/
Depends on: libevent
/usr/local/Cellar/memcached/1.4.6 (8 files, 156K)
You can enable memcached to automatically load on login with:
mkdir -p ~/Library/LaunchAgents
cp /usr/local/Cellar/memcached/1.4.7/com.danga.memcached.plist ~/Library/LaunchAgents/
launchctl load -w ~/Library/LaunchAgents/com.danga.memcached.plist
Or start it manually:
/usr/local/bin/memcached
Add "-d" to start it as a daemon.
http://github.com/mxcl/homebrew/commits/master/Library/Formula/memcached.rb
alias memcached-start="launchctl load ~/Library/LaunchAgents/homebrew.mxcl.memcached.plist"
alias memcached-stop="launchctl unload ~/Library/LaunchAgents/homebrew.mxcl.memcached.plist"
alias memcached-restart="launchctl unload ~/Library/LaunchAgents/homebrew.mxcl.memcached.plist;launchctl load ~/Library/LaunchAgents/homebrew.mxcl.memcached.plist"
and after that you cant easy start/stop/restart memcached