I concur with Rocker -- clove oil is best because with the fish staying still, you need to apply less pressure when holding it, and hence are less likely to bruise or damage the fish.
Here's some general advice: Do a "dry run" first. This will let you test the system out, while applying less stress on the fish (and you!). Put the aquarium water in a 1 litre tub (ice cream tub for example) and add 2 drops to the water. Stir well. Catch the puffer, put it in, and then see if it becomes sedated. Sometimes you need more clove oil, but do bear in mind that a massive overdose will kill the fish. That said, that's something like 10 or 20 drops per litre. Do not add extra clove oil while the fish is in the water. Remove the fish, add the oil, stir well, then return the fish.
Anyway, once you've seen the fish calm down, take it back to the aquarium, and float the net in a strong water current so that lots of oyxgen gets into the fish and "jump starts" it.
Now you've seen how the system works and tried it out, repeat the next day. Use cuticle clippers. I bought some from Boots for about £5. The "art" to doing this is holding the fish gently but not with force. That's why you want it sedated. If you squeeze it, you run the risk of causing damage to the internal organs. Try and clip the teeth with the clippers, but less is more. You don't want to risk cutting the lips. Often, simply cutting away the very tips will be the easiest option. Better to do the job 4 times a year without harm than trying to cut the teeth right to the base but damage the fish in the process.
It honestly isn't difficult, but the first time is very nerve wracking for both you and the fish.
Cheers, Neale