Depending on whether your fire pit is wood-burning or gas-burning, you'll need to buy wood or gas to fuel the fire. A starter log is a great way to get the fire going quickly if it's a wood-burning fire pit. Also, it's probably good to get a fire pit mat if it's wood-burning since the embers and ash can ruin your grass.
Although most fire pits come with them, mesh spark covers, and fire pokers are also handy for wood-burning pits.
And, no matter what kind of fire pit you have, it's always good to get a waterproof fire pit cover so that it won't rust from the weather. They sell covers in all kinds of shapes and sizes, so you'll be able to find one for your fire pit.