It can be hard to pick up, but the shadows on the wall behind the backdrop in a couple of shots should be telling you that there is a light immediately behind the subject. There is one picture with the subject over a large puddle or pool of water, and that one's the giveaway: if you look at the reflection, you can see that there is a small light stand in front of the background.

As for exactly what kind of light, well, anything you could carry around in a small over-the-shoulder bag would do. You'd probably want an umbrella or small softbox (or split the difference with a Halo-type brolly box) on your subject if you're shooting under similar conditions using flash; light can be awfully dramatic in the darkness even when it's relatively big. The background light can be anything that can cover the background.

What the photographer actually used is unclear, but it does seem that he wanted to be as conspicuous as possible. That would lead me towards thinking about small video lights rather than, say, speedlights if the object of the game is to set up and have your subjects come to you, knowing sort of what's going on. (It also gives you the option of video to record a compelling story.) But that puts greater demands on the camera if you want reasonable shutter speeds; great gobs of delicious bokeh will kill the context, which is probably the opposite of what you want.

With a couple of cheap manual speedlights, three lightweight stands, a brolly and an older camera (a kit lens would probably do the trick easily since you'll probably be shooting at f/8 or f/11; a decent compact would be both less intimidating and less tempting), you're not risking much if things go bad. If you already know how not to look and act like a would-be victim, that's not as big a concern as some people might think, but it is still something to think about. It's really easy to give off the wrong vibes, or not to read the scene well, and wind up hanging the equivalent of a "free saleable gear here" sign around your neck. If you know the territory and the territory knows you, you can relax a bit and just use common (street) sense.