The nearest train station is Clapham Junction which is a 25 minute walk, or you could get buses 35/37 or 345 to Clapham Common.
Clapham Common and Clapham South which are both on the Northern Line (Zone 2) are short walk to the Common.
On the Overground, Clapham High Street is also close, you can walk it in 20 mins, or you can get buses 50 and 155 which takes 10 minutes.
The following routes run near to the common: 35, 37, 50, 88, 137, 155, 249, 255, 345, 355, 417 and G1
Night buses include: N35, N37, N155, N137 and N345.