DerekB, you've pretty much described my situation at around your age, although I continued to ignore that part of my life for a few more years into my twenties. Only recently I started working on getting more success with women. I haven't gotten there yet (far from it), and there's plenty of good advice here from people a lot more experienced than me, but maybe I can share a few little things that did help me get a little bit more success:
1) Instead of asking a woman out, try just casually inviting her to do something. For instance, instead of saying something like: "Are you free on Saturday? Would you like to go to a movie with me?", I'd drop in the middle of a conversation: "Hey, <movie name> is on at 7 tonight. You in?". It sounds more like "I'm going anyway, would you like to join? It'll be fun!" rather than a date. Can be anything, doesn't have to be a movie.
2) Eye contact can help you know if she's interested. If you are attracted to the girl you're chatting or going out with, you'll naturally want to look into her eyes longer. Do it, and see if she does the same and smiles at you. If she does, you can try holding hands, or whatever. If she follows you, keep moving forward in small steps. If she's not interested, she'll let you know in a friendly way.
3) The "getting out there" thing, like your friend told you. It seems like an oversimplification, but it's true. I didn't go out for parties much, but then one random night in a town I had never been to before, I was at a party and a pretty girl invited me to dance and we ended up kissing. Pure luck, but I think it's an example of how just being out there can present lots of opportunities to you.
Those are the things I've done so far that have worked for me. The hard part is that when you haven't had much success, each rejection or failed attempt hurts a lot more than it should. I guess the only thing you can do is stay strong and keep trying. Best of luck!