Been there, done that...
In my case it was the middle of 3 chainrings. I have a new replacement ring, but for reasons which are not relevant to this question, have chosen to file the teeth (twice
).
If you want to try it, you need to understand which part of the teeth needs to be modified. The chain sits at the bottom of the teeth. It will stay there unless the driving faces of the teeth which push the chain aren't radial enough. Think of an idealised tooth form, which is a circular arc at the bottom (to fit the chain rollers) & the upper part of the teeth is a series of straight radii. It wouldn't work in practice, but the geometry means that the chain contacts the ring on faces which are radial. That's the shape you need to work towards at the bottom of the teeth.
In the worshop you need to have a rat-tail file with the same diameter as the chain rollers; a couple of mm oversize shouldn't be an issue. The technique is to file circumferentailly on the worn faces of the chainring. I advise clamping the ring with the crank side facing you & the tooth you're filing horizontal (3 o'clock). Then file with pressure downwards, though with some bias (I can't quantify what I've done by feel, I'm afraid) towards the centre of the ring to counteract the file's tendency to wander towards the ends of the teeth. For my chainring, 3 or 4 strokes with the file was enough. That's a 9-speed chainset with thin teeth & it wasn't very badly worn. If you choose to tackle yours, which I suspect has full-width 3/32" teeth, you'll need more strokes. Don't overdo it, or you'll end up with a ring that doesn't want to let go of the chain at the bottom, commonly known as chainsuck, & tends AUI to trash the rear mech.
Finally, to reinforce what Brucey said, never file with pressure towards the centre of the chainring.