This can be achieved using AutoComplPop (vimscripts, old / Github, somewhat old).
The number of characters needed to be entered before it'll try keyword completion can also be set.
let g:acp_behaviorKeywordLength = 3
Note that the the newer versions requires the L9 library. The old one at vimscripts does not.
It's kind of confusing since there's different versions on all the different sites (vimscripts, github, bitbucket).
Install the plugin(s) using your favorite plugin manager.
Personally I prefer Vundle, but Janus uses Pathogen.