Generally depending if you are in test design or test development.
(tasks are interchangable depending on company)
test design>>
Test structure definition and specification
implementation of DFT (scan, BIST, boundary scan, macro test, etc)
ATP generation
pattern simulation
test development>>
Pattern conversion/cyclisation to ATE format
Test program generation
Tester board design
ATE testing
Test program transfer to manufacturing site
The former sits in the office facing the workstation, the latter ferries between office and test site, usually in the wee hours, but gets better renumaration.