If you are traveling by tube the nearest station is Hammersmith on the District or Piccadilly Line. Exit out of Hammersmith Broadway, which is the main exit, and turn right. Continue walking along Hammersmith Road towards Kensington Olympia. You will pass a L'Oreal building, a Holmes Place gym, and a pub called Latymer's. Colet Court is a terracotta colored brick building directly across from Latymer's pub.
You may also use the Hammersmith & City Line station. Take a left onto Hammersmith road. You will pass Good News Agent, the Lunch box café, and numerous little shops. On your left you will find Colet Court after about a seven minutes of walking straight up the road.
Alternatively, you may travel to Kensington Olympia train station. From here you take a left from the station, walk straight up the road, where you will hit the bottom end of Hammersmith road. Turn right up Hammersmith road and walk straight for about 10 minutes until you hit Colet court (see above for description) on your right hand side.