Yes it can be done. I personally do minor fret-work myself, using a blunt-edged 3-sided file, a bigger file, some steel wool and metal polish. But would not recommend it to first timers since its quite easy to mess it up.
There's a difference between un-levelled frets and worn out frets. If your guitar is old, and as the issue suggest, you are facing a worn-out frets issue. The only way this could be rectified is fretting afresh with new wire. If someone says it could be done by grinding/polishing etc etc, they may be incorrect since your fret heights would drop to lower levels affecting playability. Check the neck. Is it warped/bent? That could be one of the reasons also.
How one would go about it is (if a complete re-fret is not being done).
Please tape your fretboard/pickups with surgical tape or some other kind which does not leave sticky residues.
a) Level the neck through truss rod adjustment.
b) Take out the strings, and check the heights of individual frets. I use a "rocker" constructed out of the credit-card-size plastic that comes with sim cards attached to it. You place the plastic-card on its edge so that it covers 3 frets, and the "rock" the card side to side. If the middle fret is level with the other 2 frets, the card should not "rock". If the card rocks, it means the middle fret (fulcrum for the card) is at a higher level then the 2 frets on either side of it and needs grinding.
Grinding should be done with diagonal movements. Why? See point (d).
c) Once the frets are level, you "crown" them using the blunt-edged 3-side file. Slow and light movements are best. The blunt side prevents tarnishing the fretboard. Using light movements from side to side, re-crown the frets
d) Steel wooling should be done to achieve the shine on the frets. Steel wooling should be done along the length of the frets. This makes the steel wool rub at an angle to the grinding-marks left by the file in step b. Because of the angle, the steel-wool is effectively smoothening the filing-marks. If the pickups are not taped, steel wool might attach it which is a pain to remove.
e) Polish the frets using a simple metal polisher. Remember, less is better as you don't want anything flowing into the fret-seats and unseating your frets, or reacting with the fretboard in some other undesirable way.
f) Oil the board. I exclusively use Fret-Doctor.
Disclaimer : Please do this at your own risk. Noone will be responsible if you mess your own guitar. This can be very easily messed up and needs to be done with a very light hand
Having said all that, take your guitar to a guitar shop which has a luthier. If he recommends a refret, you could try out the above since if you mess up with the frets, they are gonna be refretted anyways. But plz plz plz, don't mess up your board.
My gear, currently up for sale
Washburn X-16 anarchy - SOLD!!
duncan pickups - I wonder why Im selling these.