Please note there are improvement works on the Jubilee line this weekend, so the tube to North Greenwich will be shut on Saturday and Sunday.
It's incovenient but far from a disaster - here's your alternatives:
1) Get the boat: Easiest public transport option if coming from Central / North / West: The Thames Clippers run every 20-30mins from Waterloo / London Bridge / other Central london piers - check the timetable. It's a very pleasant way to get there, and the jetty's not far from the main entrance.
2) Get the rail replacement service: Easiest public transport option if coming from east, and probably quickest for all - get the tube to Stratford (Central line) or West Ham (Hammersmith & City / District line), then get the Jubilee line replacement bus - which goes straight through the Blackwall tunnel to the dome, stopping only at Canning Town en route.
3) Get a bus: There's a bunch of bus services to choose from: 108, 188, 129, 472, 422, 161, all of which service North Greenwich. The 188 goes from Holborn, through Waterloo and Elephant & Castle, straight to North Greenwich. The 108 goes from Stratford, through the Blackwall Tunnel (though the rail replacement service will make less stops if you can get that).
4) Get a cab: Easiest and quickest option all round, the best option for those travelling later on, and not necessarily too expensive - matter is really quick and easy to get to from the Bow area of East London - the Blackwall tunnel approach intersects with the end of Bow Road. We would recommend meeting in a group somewhere east, and booking a cab from there.
Unfortunately these Jubilee line works are set to continue on and off for the next couple of months - how we will rejoice when they're finally over! But hopefully it needn't be too much of a problem for you, and if you plan to get the boat and the weather stays nice it'll actually be a bonus!