There is a lot that can be said on this subject, and what works for others won't necessarily work for you. In order for you to develop your own approach, you need to be aware of exactly what needs to be achieved. To my mind, your approach should establish three things: attention, rapport and control (or what I've just decided to call "the approach ARC"), and it should do this within about five seconds.
Attention is easy to get but harder to keep. You could get attention by doing something crazy or flashy, but that doesn't necessarily lead to good rapport, as it can be intimidating, which means you'll lose your audience quite quickly. The ideal situation is to get attention without magic, or a mention of magic, so people are engaging with you as a person, rather than just with your tricks.
Rapport is something that whole books have been written about, and you can go really deep into pacing and matching and mirroring and all that, but essentially, all you need to do is smile, make eye contact (but don't stare) and hold a normal friendly conversation. People like friendly people, so that's really all you need to be. Don't worry about putting on a character to begin with, as it will come across fake and inhibit rapport. Allow your performance persona to develop naturally as you gain more experience.
Control comes with confidence. Not arrogance or confrontation, but a sense that you know what you're doing. You can take control of any conversation with questions, because when you ask a question people have to take a moment to think of an answer. While they're doing that, a follow-up question or an instruction will immediately make you the dominant one in that conversation.
If you're performing on the street you should ideally pick out your prospective audience from a distance. Then, rather than marching straight up to them, which can be threatening, act as if you're going to walk past them then, at the last minute, turn and catch their eye as if you've just had the idea to talk to them. Smile walk towards them. The line I use is along the lines of "Hi, how you doing? Has anyone shown you any magic yet today? No? That's no problem I can sort that out for you right now...I'm Tom by the way, what's your name?"
As you can see, it's basically a series of questions, although at no point have I asked whether they want to see any magic. I've just led them towards that result. The "Hi, how you doing?" is just a nice friendly opening, to which social convention demands a friendly response. The quick, slightly confusing, follow up "Has anyone shown you any magic yet today?" contains the implication, with the "yet", that it's inevitable, they will see some magic at some point. Then "That's no problem..." is a response that implies they've actually requested to see something. At this point they could potentially raise an objection, so I cut that off with "I'm Tom by the way, what's your name?" It's another friendly question, which, when accompanied by a handshake, seals the deal that some magic is now going to be performed.
Oh, and the other thing I should say is, your first few performances with be absolute garbage...no disrespect, but it's the same for everyone. You will be rejected, you will screw up tricks, you will get blank looks rather than gasps of amazement. You just have to stick with it and keep performing as much as you can and it will become second nature.
Hope some of that was helpful.