Strummin has some good advice about mic type - that's something that a lot of folks don't think about, if you place the monitor to the proper place according to mic type, you'll get much better monitor volume and tone before feedback.
It's good to have the signal as hot as possible so you can work your distance to the mic effectively - it should be hot enough that you can be up on the mic and sing without have to belt out at the top of your lungs and then find the spots as you start to belt out more. Randomly belting it out right up on the mic will likely cause the sound guy to turn down your gain or your level. Be conscious of distance v. singing volume. Varying dynamics makes you sound more polished.
Know your mic - it's always a good idea to bring your own even if someone else is running sound. Know how the tone changes as you get off axis - can be good if used consciously or bad if you do it unconsciously. Know where you need to be distance wise as you change singing volume. Know where it needs to be placed relative to your monitor. All mics are different. Also, be aware of some of the most common mics you are likely to encounter if you don't use your own. Most likely it will be Shure SM57 or SM58. Most sound companies don't shell out for condensers that some dweeb is going to think he's Roger Daltry and start swinging it around or spitting 20 beers into, etc. If they do have nice mics, learn what they are and treat them accordingly.
EQ is super important - a lot of sound guys I have encountered over EQ vocal mics erroneously thinking that when someone is asking for more volume what the really need is more definition which can be accomplished with EQ. They then crank up the gain or level and scoop out the EQ because it feeds back. This takes out a lot of the frequencies where your voice is strong and can make it harder to hear even if it's at a higher level.
Practice with a mic - I was forced to learn to sing on stage and it's still very much a work in progress - I thought I had my parts together then when you get into a mic everything sounds different. It sucked. As I got comfortable with a mic it sucked a lot less - even get some compliments
No fear - Go for it! You have nothing to lose. If you do you might tank it but you have a chance of nailing it. If you don't go for it you have very little chance of nailing it. You are likely a better singer than 90% of the people in a crowd, even a weak stage singer is better than drunks in the crowd. Have some attitude - don't be a dick, but have some attitude and confidence.
Remember, if your covering Dead tunes - they were a pretty inconsistent vocal group too - your not covering Pavorotti. Don't worry if it's not 100% perfect - strong finishes can make up for some early tweaks. Have a really bad short term memory - if you fuck something up, forget about it and move on. Don't let a mistake cause you to give up or to get you down.
HAVE FUN WITH IT!!!