Try an open-mic night. I went empty-handed to one, and after I saw there were people worse than me who got up, that was enough for me to try it the following week. I took my music with me because I was afraid of getting lost. I only had to refer to it for the first line of each verse, but it took out a lot of that fear.
One funny thing -- if you're nervous and sweating, and there's a hot light shining on you, that will make you sweat even more which, in turn, will make you even more nervous! So stay out of the friggin' light!
I'm not nuts about my voice. I tend to sound like Neil Young and consequently play and sing mostly his music. However, when I play in front of others, I try not to play him, because I don't want to hear, "that sounds just like Neil." If I play a song of his, I try to pick an obscure one, so no one will know!
I also try to play new songs that I haven't already played 100,000 times on my own. I like to think they sound fresher. Sometimes it sounds better because I have yet to discover the things that trip me up.