There are two Paddington stations (strange) so I don't know if you'll be taking the Circle line or the Hammersmith & City line, but no matter which one you take, they both go to Baker Street station. That's where you drop off. Then follow the directions on that station to change to the Jubilee line. Then catch that tube and drop off at North Greenwich station. If I'm not mistaken, the O2 should be to your right. But let's hear it from someone who lives there, because I've only been there once, in 2007.
As my tourist-book-map is packed with the rest of my stuff right now (my place is a mess because of renovation works) I can't tell you the directions of the tubes (Northbound, Southbound, whatever) because I have it written down. But people there are very nice and they'll help you if you ask for directions.