When you get off the train, you will need to head off the platform and exit the building to your left to head towards the correct bus stop (follow the orange lines in the attachment).
You will need to catch either the 11 or the 12. The 11 will be heading to Leamington Spa via the University and the 12 will be heading just for the University of Warwick. It will cost either £1.80 or £1.90 for a single (it seems to change based on the day and the bus driver
) and it's exact change only.
You will need to get off the bus at the Sports Centre bus stop. It will look like the attachment and the bus stop is circled.
Then cross the bridge (you can just about see in the previous attachment and the building is the one in the far corner!
(Note: That last attachment has quite an outdated satellite image. The building works you can see slightly to the right of the lines are now complete, and there's a new building on the grass patch at the back).