Tube is NOT free. If you have a travelcard season (as opposed to pay as you go) that includes zone 6 then it covers journeys between the three airport stations so it won't cost you anything. It will if you don't have a travelcard. You will however need to change trains at Hatton Cross if travelling TO terminal 4 as the Piccadilly line does a loop.
Heathrow Express is probably best between T1/2 & T4 or T5 where it is free although there is a bit of a trek to T3. Annoyingly there isn't a direct link between the Central Bus Stn & HEx - the entrance is on the pedestrian tunnel route to T3 Arrivals, about a five minute walk.
Buses are probably best between T4 & T5 landside (also free) as you have to change HEx trains.
There are buses between all terminals airside so its not an issue if you are changing planes.
Last edited by Peter47; 12th Oct 2013 at 09:25.
Reason: Clarification