Hi, I'm no singer either.
When I start I'm writing the melody in my head and singing to myself. For me songwriting is iterative to get the music, lyrics and structure together.
If you're demoing it for others to sing then you either have to give your vocal line as a guide, or with piano you can play the vocal lines. With a guitar I multitrack and put lead as a guide for the vocal line.
My view is if it kinda of works with someone with limited vocal abilities then when you give it to a good singer who likes it, it will only get better, and at that stage I have to let go...
One piece of advice someone gave me was around practicing, the more you write, play and sing etc the better and more confident you'll get. Professionals songwriters will be writing a new song every day..
I'm sort of wondering was there something specific that prompted you to ask?
Sorry if thats a bit rambling but hope it helps.
Neil