I work in Illinois and have an apartment here. I also have a house in Georgia and travel back and forth between the two residences. The tax form asks for dates of partial residence. Do I enter 1/2 a year?

You need to determine whether you are now a resident of IL or of GA. In general your resident state is the one you spend the most nights in. It sounds like this makes you a IL resident, as long as you're your job is a permament one (not a temporary assignment). If you are a IL resident, you fill out IL's resident return and do not need to file with GA at all. This is what I do - I live in IL and have a second home in NJ, which I visit pretty regularly, but since I work in IL and spend the most nights here, IL is my tax home. It's helpful that IL's tax rates are lower than NJ's (and GA's as well).

On the other hand, if you are still a GA resident (perhaps on temporary assignment in IL) then you fill out a GA resident form and a IL non-resident form.