I live in Athens, Ga and I am a student.
I've been living up here for the last 4 years, and I will stay in this town for extra 2 more years to get my masters in food engineering (yes, to make MREs)

I want to apply for my CCW, and probate court website says "you have to be permanent resident"

How do i declare permanent residenship?

Check with your own state, as the requirements differ from place to place.  Here, for example, for CCW purposes proof of residence is a state DL or ID dated at least 6 months ago.  Another place I was it was 2 consecutive months of utility bills.  

In Fl. its three months utility bills.

damn good question!  Usually a DL issued in the state of physical residence is all you'd need....different states have different rules about how long you have to have been living there.  

Try Packing.org for a list of who to contact.  I've found that the Sheriff's clerk is pretty helpful with things like this.

Have you voted there?
If you've registered as a voter there that might work.

Definitely check with the government offices in your state to get the right info.

Proving residency is an interesting issue.  Sometimes it depends on what it is you're trying to do that requires proof.
When I lived in Alaska, if you wanted your dividend check (oil money dispursment for Alaskans), you had to 'PROVE' you intended to stay in Alaska permanently.  This seemed to get students and military personnel into all kinds of tight spots.  It was easier for someone like me who didn't belong to a group associated with frequent moving between states.

Do you have a job?  If you list 'student' as your occupation, this might be a flag to the state that you are not intending to stay in Georgia permanently.

The voter registration card is a good proof of residency.

I'll second that little bit about Alaska and proving residency....was stationed there for a few yrs and it was like pulling teeth!

For me, as a resident alien, my Fl CCW and DL are not proof enough to purchase guns from my FFL who's known me for years. I still have to give him copies of my utility bills to prove residency. ATF even gave him a little grief over not requiring it from me but yours is a different case.

varies from state to state, iirc Georgia isn't too hard.  South Carolina on the other hand is rediculous

I just applied today.

The court clerk asked me "are you at least 21 and permanet resident"?  And i said, "yes ma'am"

that was it.

Thankx guys.  I guess I will have my CCW in 90 days or less. YAY