Been wondering about this myself lately, so here are a few tips:
1. Try to talk to everyone, or at least anyone you have something immediately in common with. This opens the doors to getting to know them better and improves your chances of deciding whether they're friend material (I'm still working on this one myself, I have very bad SA sometimes, and not so bad others, but just keep trying)
2. If you decide that they're friend material, and think that this feeling is reciprocated, then do everything to be as open and honest with this person as possible. If you get a phonecall pick it up or ring back, if you get a text, text back. And initiate as many potential meetings as possible yourself, so the other person doesn't feel like he's the only one trying. It's hard, for me at least, but it gets easier as you get to know them better.
3. Try to hang out with the person as much as possible, the more the better since that way a natural friendship can form quickly, but even if it's only once or twice a week that should be fine ( a friend should also be able to understand your needs). Invite them round to your place or go to theirs, or even better find something to do outside the house. The important thing isn't what you do, it's that you're doing it together.
4. Be yourself, don't feel you need to do/say things just to impress them. This is probably the hardest point for me, as i hate silences or not having anything to reply to something they've said, so I might make up something or pretend to be a certain someone in the vain hope to impress them. It doesn't work, if you just act like yourself people will appreciate you for it.
5. Learn as much about the other person as possible by setting the right questions. Maybe write some down some which you can use all the time. Listen carefully to what they say when they answer your questions, it could be used to lead into further conversation or so you know what to get them for their birthday in future lol; don't get bogged down by what you're going to say, this should come naturally if you listen carefully. Also, reveal as much about yourself as possible.
6. Become a little more curious in the world. Read a newspaper every morning or something so that there's always something to discuss on your mind. Decide on a right time to bring them up.
7. Don't worry about how a meet-up is going, or whether or not the other person in bored. If you enjoy yourself, the other person is also likely to enjoy themselves. Also don't blame yourself for any perceived failures (awkward silences, not knowing what to do, etc). I come across a few instances where people have phoned me back after what i thought was a failure (i.e i judged myself too harshly, the other person did not)
8. Remember that this is all just theory, and that in the end it's about having some confidence to do the things you're not comfortable doing, and trial and error.
Hope these pointers lead to long and fruitful friendships for you

Good luck!