I am a resident of Texas and worked there for half of 2007. The other half I moved to South Carolina and am working full time and attending grad school without establishing residency. I have received both W2's for the year. One with my Texas address and one with my South Carolina address.

What process do I undertake to file taxes for this year?

Also, is there anything else I need to do since South Carolina has a state income tax and Texas doesn't?

Check out this site it might be able to help you with your question
State Income Tax Returns - Tax Tips from TurboTax
Hope it helps!

You have to file a SC tax return for the money earned in SC.