It's totally straightforward, you'll be given a form on the plane to fill out. An image is at

http://www.jacustoms.gov.jm/docs/n_C5Update.pdf

The front is your immigration form, and the back is your customs form. You will keep the bottom part - it's marked "Departure Record" - for your return flight. You are specifically asked on the form whether you are bringing gifts (item 6 on the Customs side). You may be charged duty on what you are bringing - anything that will stay in Jamaica and not go home with you may be subject to duty. Sometimes you get charged, sometimes you don't; as long as you've made an honest declaration of entry, the agent's decision is binding (meaning they can't come back later and change their minds on duty if the agent said something was not dutiable).

I have never encountered a problem, or much in the way of questioning, on departure. Of course, when you get back to the US, you will be dealing with US Immigration and Customs regulations.

One weirdness is lighters - on departure from the US, you can have them in your pocket but NOT in checked baggage, on departure from Jamaica they will take them away from you.

A false declaration of entry is a good way to spoil your day (or more), in EITHER direction (I have personal knowledge of someone who thought he didn't have to write stuff down coming back into the US and had everything confiscated).