Drinking alcohol does make you ease up a bit, but there's a fine line between getting nicely tipsy - where you're sociable and fun - and stupid tipsy, where you end up hitting on everyone and saying things you'd really rather keep to yourself. Also it's hard to decide how much to drink, and even if you're aiming for nicely tipsy it's easy to go overboard and get drunk (sometimes it takes awhile for you to notice) and once you've drunk too much there's not much you can do to undo it short of a) making yourself puke, b) drinking lots of water and eating and waiting til it wears off.
If you're underage well I'd never really recommend it but if you're not, a couple glasses of wine would relax you. I can't say how much you'd need to drink because it depends on so many things, including body mass, alcohol tolerance/experience, and how much you've eaten and how well-hydrated you are. Make sure to eat dinner and that you're not dehydrated. Start with one glass, drinking sloooowly, and wait and see how you feel. Make sure your head doesn't feel too heavy and that you're still thinking straight!