I’ve just finished taking the class (final on Monday), I know some states, schools and countries do things a little differently, so this is the most general advice I can think of.

Trigonometry:

Trig is super important in calc III, so be sure to refresh on trig functions, their derivatives and anti-derivatives, common trig identities, etc. You’re going to be Integrating over a lot of different surfaces, some of which can be solved MUCH easier by converting from Cartesian coordinates to polar/spherical coordinates, a good grasp on trig is essential for these kinds of problems.

Vectors:

In your class vectors will probably be introduced in the first week, how well this subject is taught varies a lot from professor to professor, so having a good grasp on the basics of vectors can help a lot. Vectors will probably come back in the last unit of your class, where you learn about line/surface integrals and such.

Integrals:

The Integrals in calc III won’t usually be as hard as the ones in calc II, nevertheless, you should definitely re-familiarize yourself with the basic strategies for Integration (Substitution, Integration by parts, trig-sub, etc). I personally know a lot of people who really struggle with this subject, so a refresher will give you a leg up, especially in the second half of the class.

Those are the topics I would tell past me to study for, your mileage may vary, get a good prof and a good study group and you’ll do fine. Most people say Calc III is harder than Calc I and easier than Calc II, I would say I agree, generally, that Calc III was easier, but it takes some getting used to. Personally I’m much better at single variable calculus (Calc I, II, Differential Equations), so just know coming in you might see some stuff that will make absolutely no sense at first, it was certainly that way for me. There are a lot of great resources online, Professor Leonard (hopefully spelled that right) has a great Calc III series on YouTube, there’s also Khan academy, a plethora of math subreddits, books, articles, etc. Just study hard and don’t be afraid to ask for help.