The RailAir shuttle bus leaves every 20 minutes (30 minutes on weekends) and goes directly to Reading with no intermediate stops.
From Terminal 5 (the British Airways terminal) you can catch it outside Arrivals (typically from bus stand number 9).
From Terminal 4 you will have to catch the free Heathrow Express rail shuttle service to the Heathrow Central Bus Station. Travel in the carriages at the rear of the train and alight at Terminals 1, 2 and 3, and follow signs to Heathrow Central Bus Station.
Alternatively, you can catch the free bus routes 482 and 49 to Terminal 5 and catch RailAir from the bus stand 9.
From all other terminals you have to walk to the Heathrow Central Bus Station, follow signs for local buses upon exiting Arrivals. Using the conveyor belts it is a short walk through a tunnel.
Tickets can be purchased on the bus, but they may be more expensive.
In Terminal 5, tickets can be pre-purchased from the National Express Sales Desk which is located inside the terminal building opposite Costa Coffee (turn left out of Arrivals).
You will find bus stand 9 by exiting the terminal building opposite the National Express sales desk.
When purchasing the ticket ask for "RailAir service to Reading".
You can purchase tickets ahead of time online here. This will generate an email which serves as a ticket to be shown to the driver when boarding the bus.
There is also an app from First Bus called mTickets and can be downloaded from the App Store or Googleplay.
In the app, a search for 'RailAir will give the correct options (Heathrow to Reading and Reading to Heathrow). A period return ticket is £25. That takes you from Heathrow to Reading and back. Returns can be made within three months time. There are also single tickets.
The bus lets you off at the main train and bus station in the center of Reading.