If you are in a big city then I recommend going to social events on Saturdays and not on Friday evenings (people haven't recovered yet from work-week stress.)

Also keep in mind that most people are mentally preoccupied with themselves so aren't thinking about you. Despite appearances, social anxiety is normal which is why alcohol is usually served. Most people at a social event will be there because they want to talk to people such as you, so if you can appear calm and are interested in what they have to say then you will seem like a natural. If after twenty minutes you aren't having fun then just leave early.