I've been doing this for years and in my experience the best way to start doing this is:
[b]-Start by singing and playing along with songs sung by the bass player.[/b] E.g. The Police, Rush and that kind of stuff. If they can do it, so can you. They usually make bass parts that are easy to sing along with. I love songs like Message In A Bottle.
[b]-Start singing lead lines with songs you know (while playing of course).[/b] Those are the vocal lines you probably know best, so you don't have to think too much.
[b]-Take the backings![/b] Mostly you'll want to just add a third on top of the lead melody. They're the most widely used way of singing backing vocals.
[b]-Take it to the next level: talk.[/b] Talking and playing is the hardest thing to do, because talking isn't a musical thing. If you can do thát, you can sing and play any rhythm.