To expand Tichfield's answer:
Take a westbound Piccadilly Line train to Leicester Square. (Under 10 minutes)
Change to a southbound Northern Line train to Waterloo. (About 5 minutes)
Take a South West Trains service to Teddington. (About 8 trains per hour. Journey around 35 minutes).
Turn left out of the station and walk 300m to the High Street.
Turn right and walk along High Street. As you continue straight on, this becomes Ferry Road. When you come to the main road (A310, Manor Road/Kingston Road), go straight over and you'll come to Teddington Studios on your right. (This bit of the walk is about 800m. If you prefer imperial units, the entire walk is about three quarters of a mile).
If you hate walking, take the train from Waterloo to one stop further along, which is Hampton Wick. From the opposite side of the High Street to the station, take a 281 or 285 bus to the junction of Kingston Road and Ferry Road. (Approaching from this direction, you'll need to turn right onto Ferry Road, which brings you almost directly to the entrance to Teddington Studios).
Allowing for time to work out where you're going, and waiting for trains or buses, you need to allow at least 1� hours for the journey.
Chris