Are you connecting to another flight from Terminal 3, and can you get your bags through-checked? If so, you might as well follow the Flight Connections route and stay airside. The process is:-
- Follow signs for Flight Connections Terminal 3
- Be taken by airside bus to T3
- Clear security
- Go to transfer desk (if necessary) to get new boarding pass
- Go to gate
If you can't get you bags through-checked, then you will have to clear immigration, collect your bags, and clear customs. Then, as Rollingthunder says, take the Heathrow Express to the next station which serves Terminals 1, 2 and 3 and then follow the signs for T3.