First & foremost, what holds true for Apocalypse World mostly holds true for The 'Hood as well, with just a few tweaks here and there: the agenda remains the same, so make The 'Hood seem real, make the players' characters' live not boring and play to find out what happens. The streetplan of the 'hood is your best tool for making it seem real: you've got a map right there with everything important on it, as well as a list of important things that aren't on it but exist outside its boundaries. Make that plan the centrepiece of the table and when anyone does anything, ask them to point out where they are when they do it; better still, get them to show you how they get from A to B and fill in the alleys and shortcuts of the 'hood as you play. The streetplan shouldn't be a static document, it should change organically as the group discovers what it needs and adds it to the map; once in a while, ask the players a directed question, like "Who do you pass coming out of the bookmakers?" or "You bump into your cousin; where's he headed to?" Add further locations to the map or the list of places that are beyond it when they come up in the fiction.
Another tool you can use is a contacts list: ask each of the players to keep a list of who's on their character's phone and make sure you have copies of those lists. The contacts list is a double-edged sword: it establishes in the fiction who the PCs can quickly and easily get in touch with, but of course those same people can easily get hold of them. Making calls on the mobile/cell is a great way to frame moves like ask around, plan B, take the heat off and lie low, but also a great way to bring up the PC's payback box at the absolute worst possible time. Add some fun details to this technique by asking them what the ringtone is on their phone and whether they have different ringtones for different contacts: if you can have those tones cued up and ready to play, it's a great way to instantly foreshadow the badness that is about to come down on their heads.
The characters lives won't be boring if you're handing them opportunities and problems, so do both: better still, hand them opportunities that will create problems and problems that can be exploited as opportunities. Creating PCs and NPCs should have resulted in a bunch of potential triangles, so stir them together: look for ways the NPC's genuine agendas can trigger situations which threaten the PCs' livelihoods. It doesn't take much to bring the authorities down onto the 'hood or put an NPC in the cross-hairs of some of the bigger gangs that surround it; the ways different PCs are getting by are designed to overlap, so that the action one PC takes to protect their livelihood is liable to threaten someone else's. The default assumption of play is that someone is always going to be short and looking for a way to make ends meet again, so a major aspect of the conversation at the table will concern what it takes to restore a livelihood. If that isn't happening enough, look at the payback boxes of the PCs and see if there is a way someone can demand a favour from them that puts them into conflict with one of the other PCs:
- The Heavy and The Ice put their reputations on the line and swear they will get the job done, but carrying through on that promise to an NPC can put them in direct conflict with The Bastion and The Fallen.
- The Blur, The Go-Between, The Hacker and The Rebel all need some degree of secrecy to go about their work, so the last thing any of them wants is for an ex-customer to spill the beans: if an NPC starts telling tales in public, they'll have to deal with them, one way or another.
- The Feelgood, The Merchant, The Pimp, The Schemer and The Shark all have a business model that needs customers who want what their selling: an unhappy customer might get one of their mates to make a complaint on their behalf, especially if their mate has the muscle or power to back-it up, like The Bastion or The Heavy.
Asking questions also saves you a lot of effort when you're responding to what the PCs do: there are questions implicit in the outcomes and consequences of every move already, mostly relating to who they've pissed off and how, but it's also a good way of checking that you and the players are on the same page. If they mess up, ask them "How does this go wrong?" but if they achieve what they set out to do, ask them "What does this get you?" You can think about the story as being the thing that gets you from move to move: the story follows from each move but it also sets up the next one. It matters what happens in the story, but you have to let the moves decide the direction for you and not be tempted to lead the story where you believe it should go. Talk, create, suggest, have a conversation, but use the extelligence around you (the AW rule book, The 'Hood rule book, the other players, your own prep) as well as your own intelligence and creativity.