If you haven't yet learned to keep your nerves under control, avoid approaching really attractive girls - you know, the ones who make your heart race and your brow sweat. Instead, approach ordinary girls who don't make you nervous. You'll be able to talk to them without fear. Don't worry about making them your girlfriend or asking them out on a date. Just have fun and enjoy the interaction, and you'll be amazed at your success. If they don't seem interested, just move on to another girl. The key is to NOT give up. Eventually, you'll build up enough confidence to approach even the most gorgeous intimidating girl in the room without fear.
Just be aware that because a girl is gorgeous on the outside, she may not be so gorgeous on the inside. If after approaching her, you don't like what you see or hear, quickly but politely move on. You be the one in control, not her.
As for relationships, take a cue from a very successful friend of mine, Steve, and simply be upfront about your habits and proclivities. What I mean is, tell them early and upfront that if a pretty girl catches your eye, you're GONNA look, but it doesn't mean that she is more desirable than your girlfriend. The girlfriend may not like it, but she'll learn to accept it. And, if she can't, you negotiate. Tell her that you spend every Tuesday night with the guys, and that you want to keep it that way. Tell her if you snore or fart, and ask her if she has any problem with that. By being honest and upfront, you earn the girl's respect. And that's the best way to start a relationship.