Going to be staying at a hotel near Paddington Station. Want to take the boat to Greenwich and the train back. Need info on where to get the boat and which train to take back to where? Going in the same day.

http://journeyplanner.tfl.gov.uk

should do the trick: you will need to use the options button to make sure boats are included.

Boats from Westminster, Charing Cross or Tower piers (Westminster, Embankment or Tower Hill tube stations).

Trains back from Greenwich station to Waterloo East, or by Docklands Light Railway from Greenwich or Cutty Sark to Bank or Tower Gateway; change to the Tube.

Get a Travelcard covering zones 1 and 2, and that will allow you to go to or from Greenwich by any combination of trains, tubes and buses, and also gives a 33% discount on boat fares. There are three boat operators:
www.westminsterpier.co.uk;
www.citycruises.com;
www.catamarancruisers.co.uk.
To get back by train, Cutty Sark station on the Docklands Light Railway is nearest to the Pier, Maritime Museum and the tourist part of Greenwich; trains go south to Lewisham, where you change for trains to Charing Cross, or north to Canary Wharf and Bank, both with tube connections. Services by any route back to London are pretty frequent.

We took the catamaran cruiser and enjoyed it thoroughly. The Dockland Light Railway functions as part of the tube system, so it is very accessible and can be paid for with your tube pass, as Geoff pointed out; no need to get involved with the regular trains.

An option - if you have time - is to use the foot tunnel from beside the Cutty Sark to view Greenwich from the Island Gardens on the north bank. Especially on a sunny day, it's a pretty spectacular photo opportunity (just at the moment, there's scaffolding obscuring part of the buildings, so you might want to play this by ear). You can pick up the DLR from the Island Gardens station.

If you're interested in seeing how the Brits do flood control, take a boat that goes a little further downstream to Barrier Gardens, and you will see the Thames Barrier. It's quite a remarkable piece of engineering. Then you can loop back and land at Greenwich.

We took an unusual way back from Greenwich once. A bus route traverses an area that few tourists ever see. The route is from Greenwich center and over Blackfriar's bridge.

If this were my first trip, I would take the boat from Westminster Pier and return thru the foot tunnel to Island Gardens to get the DLR and change to the Jubilee Line at Canary Wharf where I'd wander around a little.

We thought the foot tunnel was so dank and creepy, we turned back!