Do it with an instructor first. It's not realistic just to launch into US airspace and do just about the most complex thing there is, ATC wise. Class B clearances are easy, but one thing you can be sure of: if you mess it up or sound like you might, you will get a vector for the shortest way out of Class B and the instruction "remain clear of Class Bravo". This is not what you want to hear.
All Class B has an associated approach control. You will nearly always be talking to them first. You need to be familiar with the transitions available - which isn't always documented. Another reason you need to to do it with an instructor. For example at SFO you will usually get "remain south and west of the Bayshore Freeway". You need to know what that means - if you say "unfamiliar" you will get "remain clear...". They're happy to let you in and even arrange jet traffic around you (the other day a Jetblue 320 was held below me for 30 seconds or so) but the last thing they need is you messing things up for them by not following their instructions. And they are WAY too busy to vector you.
So, you contact Aproach on the freq shown on the Terminal chart, and you say "Nxxx 200o' VFR Petaluma request Bayshore transition northbound" (or whatever). They'll give you a squawk and a routing and the magic phrase "cleared into Class Bravo". If they don't say that, you should - you want it on the tape. But you need to be prepared for "remain clear of Class Bravo, state your intentions" - so you always need a Plan B.
If you're actually planning to land at the Class B airport, they'll let you in (unless you sound hopeless on the radio). Be aware that this will cost you - at least an FBO handling fee, and maybe (as at SFO) a fee to the airport itself too. (I've never landed at SFO because it would cost me ~$400, though I've been into other Class B airports). They'll vector you around to fit you in with the traffic. Even LAX is quiet compared to LHR (maybe JFK isn't, but honestly, just don't go there).
Do it with an instructor first and you'll have plenty of fun.