I am GA resident, and got paid (by non profit organisation) $6k in 2006, as Non-employee compensation, reflected in 1099 box 7. No other income in 2006, no W-2. How do I pay taxes and how much... basically, what next?

You must file Form 1040 with a Schedule C or C-EZ to pay federal income taxes.

For Georgia, file Form 500 and attach a copy of the Form 1040 with the Schedule C to the GA tax return.