(And now on the Tube and local London rail --as well as Oyster-- you can use your UK debit or credit card to pay-but like Oyster, ALWAYS touch in and out each time!)
(1) By Tube and Dockland Light Railway (DLR):
Change at Bank Tube Station (Northern Line - Bank Branch NOT Charing X Branch) or Central Line) and get onto the DLR . You may have then to change within the DLR, at Poplar. In the main, get on a DLR with Lewisham (south of the River) as terminus. One can then get off at Greenwich joint DLR-Rail Station (Oyster Card Zone 2) to the DLR. Note that from Greenwich DLR/NR Station one has a usually-packed-with-tourists walk to get to the Old Royal Observatory Picnic site. There are also DLR connections from Rail Station at Stratford and at West Ham. (If unsure google "DLR +map")
(2) By Rail:
A Sunday (usually 1/2 hourly) SouthEastern service leaves Charing X, then Waterloo East Station, right beside Waterloo Main Line (all-Oyster Zone 1) to Greenwich (Z2) - with Maze Hill (MH) Station as the stop Eastbound immediately following Greenwich. Services in the other direction come from Dartford etc.
For 2015: Please avoid London Bridge Rail Station as major works are causing disruption.Although Greenwich is not far, it is the slightly further of the two Stations near to the Picnic site-and is to the North West of the site (look on/scroll over on the Google map).Slightly nearer, and to the North East of the site, is Maze Hill (but note it is in Oyster Zone 3). Again-look on the map. Maze Hill also has fewer tourists going through it.One can, if an Eastbound train is coming into Greenwich Rail, switch over from DLR to Rail and go one stop Eastwards.If alighting at Maze Hill from Central London, cross over the bridge to the Westbound (toward London) platform, go past the (usually closed on Sundays) ticket office and leave through the small exit gate (remember, if using Oyster or debit/credit card, to touch/zap out). Turn immediately right up the hill and you'll see the "Maze Hill" sign at the top. There look left and you'll see the Park railings with the North-East entrance gate. Enter the Park and then turn immediately right. You'll pass --both on the left-- the fenced-off children's playground and then the boating lake. Just past the lake, and just past the large sundial/gnomon, you'll see on your left, a path, tree-lined on both sides.Enter the path and don't veer left or right therefrom. Up hill and down dale, you'll emerge from under trees and ahead right in front of you, high up on the Hill, is the RGO! A steep path is on your left-take it and ahead of you, you'll see the RAS pennant.
Welcome to the Picnic!