Cheapest Transport to Stansted Airport

The absolute cheapest is Easybus.co.uk

If you book far enough in advance, you can get seats from £2 each way, although they're usually around £4-7 most times and days.

The buses leave from Buckingham Palace Road between Victoria Coach station and Victoria train station.

Although the various bus options like easybus are cheapest, with London's traffic its about 90 minutes each way, so a big chunk out of your layover time.
The National Express and Terravision bus options into London can be just as cheap or cheaper than easyBus for a day return fare.

The Stansted Express train will get you into London in 40 minutes but is relatively expensive.
A hybred solution is to get the National Express bus to Stratford tube station in the suburbs of London and then get the London Underground,
There is a table of the various routes, plus prices here:
www.londontoolkit.com/travel/stansted_transport.htm