1. Take the Bakerloo line from Paddington station towards Elephant & Castle.
2. Change at Baker Street station to the Victoria line towards Brixton.
3. Get off at Green Park station.
4. Change to the Piccadilly line towards Heathrow Terminal 5.
5. Get off at Piccadilly Circus station.
This journey should take approximately 15-20 minutes depending on the time of day and any delays.
Note: There are other routes available, but this one is generally considered the quickest.