Choose music that you know very well and can perform with confidence. Save your more difficult pieces for when you have more experience under your belt.
Get a copy of an instrumental track of your song and practice ahead of time at home. Record yourself singing with a tape recorder so you can work on trouble spots.
Think about what the lyrics say. The song will come alive through you when you relax and communicate the message in the song.
Have at least one friend along to lend moral support at the singing venue. Make her sit where you can see her. Glance at her often for a supportive smile.
Pay attention to your body language. You may have the voice of a songbird, but people will notice when you don't feel confident. Even if you're terrified, pretend you're Barbra Streisand. She'd smile, throw her shoulders back and belt the song.
Try karaoke in a public place to get used to singing in front of a crowd. A karaoke crowd can be very forgiving if you make a mistake and they'll cheer you on and pay attention if you're really good. Plus, you can loosen up, have fun and really belt a song.
Remember that your moments of fame or shame will be over shortly. If you're in mid-song and performing badly, just think, "It will be over soon," and you'll get through it.