Be familiar with the area, airspace, VFR routes and landmarks. Have a FLY chart if applicable, or a Helicopter route chart. Familiarity with common routing will go a long way. In busy airspace, the less work you are for a controller, the more you're likely to get the clearance you want. In NYC, knowing the heli routes will open up a lot of options in a fixed-wing as they're all available as ways through the Bravo (provided that fixed-wing 91.119 altitudes are applied, and not the (d) helicopter exception).
As mentioned above, LiveATC is a great way to learn what VFR in Class B sounds like. If you know what to expect before you hear it from ATC, it's much less daunting.
I hear horror stories about VFR traffic trying to transition Class B's in Chicago and Phoenix, but in NYC it's a piece of cake. Professional helpful controllers. The only times I've heard "Remain clear of Bravo" here were when there were operational reasons for it...one time it was because Newark's radar was down, so additional VFR traffic would have been an undue load. Barring that, VFR traffic flies through this Bravo every day, all day. Know what you want, know what ATC's likely to respond with, and have another way around/under if Class B can't be done.
