Is there a defined sequence of events when a Buddhist enters a temple?
It depends on the temple and what part of it you're entering.

For instance, I used to be involved with my local Mahayana Temple.  Whenever we entered the meditation hall, we did the following..


Took off our shoes 
Bowed to the altar, with our hands together in front of our chest. 
After meditation, bowed each time the meditation leader rang a bell (some leaders had us do full prostrations instead).
When leaving, we turned to face the altar and repeated #2.


1, 2 and 4 were common to all the Buddhist Temple meditation halls I visited.