The best advice I can give is to just get out there and DO IT. There's nothing like continued exposure to the situation to build confidence. And always remember that they can't send you to Vietnam if you screw up!
In reality, I find at our weekly Open Mic most people are either not paying attention or are wishing the best for you. I've yet to see any "incoming" directed at a performer on stage!
I certainly agree with the advice above to practice, practice, practice the songs you want to play so they are second nature to you. As you get more comfortable on stage, you can stretch out and try some things not so familiar in your muscle memory.
If at all possible, leave the sheet music behind and look at the crowd you are playing to. Nothing puts a crowd to sleep faster than to see someone focused on their sheet music. It makes for a total disconnect from the folks you are there to play for.
For starters, go and check out your local Open Mic(s) and get a feel for what's going on. I think you'll feel immediate comfort when you realize over half the folks sing off key and none play like Tommy Emmanuel. LOL!
Here's where I play every Thursday evening (Cameron's Pub & Inn located in Half Moon Bay, CA). Nothing but FUN and great food at this place:
Half Moon Bay Coastline. In the far distance you can see a satellite tracking station. Right below it is famous Maverick's Beach where they hold the annual World Surfing Championship:
Bill