Pay just as much attention to where the note ENDS. Starting on the one is solid, but end the note with funk or it was all for nothing.
Imagine a drummer playing a kind of shuffle beat. Think about the hi hat. On the hi hat the 1/8ths are swung.
1 and 2 and 3 and 4.
So the 1 2 3 4 parts all last longer than the "and" parts. If you were to play this straight, they would all be equal. If you were to play these as broken triplets, the 1 2 3 4 would last twice as long as the "and" parts. Funk and anything that swings is right in between.
So what you have to do to get funky is to start on the one, and then release on the 'and'. Any 'and' will do.
Think of all the variations possible. For example, you can hold a note for "1 and 2" then release on the and before the snare hits. This is extremely funky. Instead of silence on the release you can hit an octave or do anything.
There is a lot more but this is where you start.