For me it works best to always start learning a song by both singing and playing together. If the exact words are too difficult, then I just howl out the melody as best as I can until the playing mechanics settle into my brain a bit.
It all might sound pretty awful at first what with all the howling and thrashing - - but it works for me.
I agree whole-heartedly with Upyerkilt's observation that you do your own version of a song and don't get all obsessive about making it sound like someone else's recording of a song. Mimicry is not musicianship.
If I want to really polish up a song after both the lyric and accompianment are firmly in my head, I find it very useful to sing it with no instrument - - I'll knock out the beat on the body and/or with my big smelly feet and sing as strong and clear as I am able - - again, it might sound pretty awful at first but it is necessary to really learn the song.
Too many players are very anal about what they do with their fingers and assume that the singing is going to 'just happen'. Too often, players are hunched over their instrument in such a way that they can't draw a full breath, much less get enough wind to sing a complete lyrical phrase.
Vocalizing takes deliberate effort (and strength)- straighten up our spine and neck, hold your head up (not looking down at your fingers), breath from the deep gut, relax your throat, and open your mouth. Good vocal technique is no mystery - posture and breathing is the key.
If you must sit down to play - sit erect on the edge of your seat (not slumped back or hunched over your instrument). I prefer to stand to play and sing - it is more fun and it's easier to breathe.
Everybody's voice is unique - as long as you sing with confidence and conviction it will sound good - at least that's what I keep telling myself.
"That darn Pythagorean Comma thing keeps messing me up!"
[url]http://en.wikipedia.org/wiki/Pythagorean_comma[/url]