Look at the base of the mass of leaves, at the soil. Can you see a ball of roots? Then it would like a bigger pot, please.
Spider plants are wonderfully forgiving creatures. They don’t much care what sort of sun they get, they tolerate a lot of “oops” on both extremes of watering (overwatering or underwatering) and since they spend so much time making their topsides lush and fruitful, their roots don’t grow all that fast. Unlike some plants, spider plants don’t need to be repotted every year. But that does mean you need to check on them periodically, and a visible root ball is the signal that they’ve outgrown their pot.
They prefer being repotted in the spring, but, again, it’s a spider plant. They’re very tolerant.
When you repot it, use potting mix and a pot about 3-4 inches bigger than the one it’s in now. Pick one that drains well, either with holes in the bottom and a saucer or one you can put gravel into the bottom (or both gravel and holes with a saucer is good, too.)
No need to get rid off all the old soil that clings to the roots when you lift it, just put some new potting soil in the bottom of the bigger pot (on top of gravel if you’re using it), use your finger or a chopstick to loosen the soil in the old pot, lift, and transplant. Fill in any remaining space with new potting mix.
The brown leaves can be pinched or cut off with sharp scissors. If there are brown tips on some of the leaves, you can trim those as well. I usually cut on a diagonal so it doesn’t look so sad and blunt. Water thoroughly when you’ve done your maintenance. When she’s gone through a big transition, I like to bring her to my sink for a really good soaking, and leave her there to drain for an hour or so. Otherwise, just water her as you’ve been watering her.
Real plant enthusiasts insist that you need to feed spider plants liquid fertilizer once a week. I’ve not found that to be the case, but it couldn’t hurt. If she’s putting out baby plantlets, she’s mature and happy and well nourished. If, at her age, she doesn’t have babies yet, she’s hungry, and needs fertilizer.
Those little babies are super easy to plant, too. Just trim one off with scissors, fill a pot with soil and press a baby into it. Water, and now you have two spider plants!