I have lots of experience gate checking a wheelchair, which is the same way you gate check a stroller, so I have a few hints:
1) Ask about gate checking when you first check in. Sometimes, they will give you a gate check tag there, sometimes they tell you to ask at the gate. If you are to ask at the gate, ask before boarding begins. If you wait until you actually are boarding, you risk mistakes in marking your tag. (You don't want your stroller vacationing in California without you if the wrong airport code is put in).
2) Depending on the airline, your gate check tag may just say to deliver it to the gate when the plane lands. Sometimes, there are other options - like delivery to baggage claim. There may also be options to have it brought to the gate or baggage at a transfer city, if you need to change planes. If you have a very tight transfer, you might not want it brought to the gate until your final destination.
3) Before you leave the stroller, fold it. Otherwise, the baggage people will fold it and could possibly break something if they don't know how. Secure it so it won't unfold. Also, remove things like umbrella holders, cup holders that are not part of the original stroller. If they stick out, they might get caught on something.
4) Strollers take a few minutes to be brought to the gate after the plane lands, so if you are among the first off, your stroller won't be waiting for you. I think that might lead to a lot of occurances of #5.
5) Forgetting to pick up the stroller. We are often the very last off the plane and on about 1/4 to 1/2 of the flights we're on, we see a stroller waiting at the gate for someone who forgot to pick it up.