What do I need to know, do, own, buy, avoid, monitor, etc.?
I know a few things, but let’s pretend I don’t.
All I know about it is that it’s a kitten. No gender, color, temperment. For all I know, it breathes fire.
Helpfull tips will be rewarded with obscenely cute kitten pics.
You definitely need a litterbox. And food. And ideally a second kitten to keep it company. 
Beyond that, maybe a couple of toys - although a wadded up piece of paper can be just as much fun for them.
Right now, I can’t think of anything else, because it’s very early and I’m still sleepy.
Food dish, water dish, scoop for cleaning the litter, something the kitty can scratch on (our cat seems to like the round plastic thing that holds discs of corrugated rolled tightly), perhaps a bed (one of our cats loved his sheepskin bed, the other ignores it), a brush, a carrier to take said kitty to the vet.
Apparently placement of the litter box can be an issue. My daughter’s cat suddenly started peeing and pooing all over the apartment. When the litter box was relocated, Miss Cleo was content to use her box again. Who knew??
Oh, and if you have places you don’t want the cat - like hanging off the lace curtains - you might want to get a squirt gun to use as gentle negative reinforcement.
I hear laser pointers are good for hours of playful fun.
Your next step is to post pictures. (I assume you know about the food and water part). Move poisonous plants and other dangerous things out of her reach.
Then make an appointment for the spay/neuter surgery.
Have fun! Kittens rule!
All hail your new Kitten Overlord 
Ditto on the spaying/neutering. While you’re at the vet for that little operation, you also might consider the prescription flea control medication (Frontline, etc). Neither kitties nor their human servants like fleas.
Oh, and this message has been said on here before, I believe. Please keep him/her inside. Kitties that go outside can run into all sorts of nastiness (disease, fleas, fights with other cats) and live healthier lives indoors in general.
Laser pointers are GREAT. Wadded up paper works well too
Introduce him to the litter box as soon as you get home (make sure it’s one a kitten can get into; the one we have now for our adult cats would be a hard climb for a kitten). Might want to “point out” the location of the water and food dish. Then let him along to acclimate. He’s already overwhelmed. Let him explore on his own (although make sure there’s no where he can get stuck…once, we “lost” a kitty. We could hear him but not see him anywhere. Eventually we found him under the bed with his head stuck in a hole in the floor boards. We had to pull him back out. It was just like that Twighlight Zone Episode!).
After a while dangle some string, the better to draw him into your Web of Love.
Oh, and here’s hoping you didn’t end up with one of those fire breathing kittens.
The day after the kitten owns you.
Kittens and cats love boxes and baskets and anything else that’s cozy and cavelike. A shoebox is fun for a kitten. So is a paper grocery bag on its side. We leave a couple of cat carriers on the den floor, with their doors open, and the cats like to hang out in them. This way, when they go to the vet, at least they have something familiar and comforting around them.
The very best toy for a kitten is another kitten. Two are actually easier to keep than one, as they will amuse each other quite a bit. They will also amuse you while they’re playing with each other.
DO NOT allow Kitty to bite or claw your bare hands in play. It’s cute NOW, when it’s a baby, but it’s painful when Kitty gets older. Wrap a towel around your hand before wrestling.
If you get a scratching post, get a sturdy, heavy one - not one of those little 2’ posts with a little base - those are too light and fall over when kitty scratches hard.
If you have houseplants, first make sure none are poisionous to cats, and consider hanging them even if they aren’t - cats like to chew plants. I have found a few that aren’t poision and have tough leaves - jade and snake plant are two that I have.
Identify a local vet, to get your kitten spayed/neutered, vaccinated, and generally checked up to make sure he/she is the happiest, healthiest kitten it can be! Even if you plan to keep it as an indoor cat, all the vets I’ve had recommend the full “outdoor kitty” set of vaccines, just in case your cat one day meets another one (through a screen door, at the vet, if you bring it to a kennel or family member that has outdoor cats, etc). Find out about emergency/nighttime vet clinics and phone numbers. Keep all your cat’s medical records in a safe place. I keep ours with our passports.
String. To play with. Kittens and string are just so cute!
Unless you know the size of your kitten, you might want to get the smallest litter box. We started out with a tiny one, so she could climb in and out easily, and eventually swapped it for a larger one (and finally for a covered one).
When you first get the kitten, show her immediately where her litter box is. Before you do anything else, just pick her up and place her in it. She might even use it right away, just to get her scent on it. A few hours later, if she hasn’t used it, place her in it again. It really shouldn’t take much more than that for her to understand where it is and go and use it - cats don’t really need housebreaking in general.
Don’t place her food anywhere near her litter box. Cats don’t like to eat where they poop (really, can you blame them?)
Now, I need pictures!
They love the dangled string and yarn, but make sure you never let them alone with it. Minx would go from playing to eating in a second (of course, this was the same cat who’s litter box would have shiny presents at Christmas time because she would eat the tinsel off the tree).
I have a huge variety of cat toys. My Samantha (and Minx before her) ignores them all and only plays with those felt mice and soda bottle caps. Go figure.
Now. I’ve given some advice. Make with the pictures!
A little flashlight is just as good as a laser pointer…and helpful in an emergency too.
What everybody else said, and learn to walk around the house without picking up your feet. Kittens often like to walk with you, and stepping on one can be very traumatic. For you! Give the kitten something that is full of your scent to lay on, play with, etc. For some reason our cats love my stinky socks. As soon as I take them off, they grab them, roll around with them and then try to eviscerate them. Better than catnip, and cheaper too.
Get the smallest litter box you can find, and the largest scooper you can find! This makes scooping faster, and makes it easier to stay in the habit.
Get a small garbage pail with a cover and keep it right next to the box. If the pail is small, then when it fills up, the bag of litter ‘n’ poo won’t be too heavy, and it’ll be easy to take it out to the garbage can or dumpster.
Not really. My cat’s reaction to a flashlight spot is the feline equivalent of “Meh.” But the laser pointer? Hotdiggitydog!!
Don’t waste any money on catnip yet - most kittens don’t react to it until they’re about 4 months old. Boxes are wonderful fun for kittens. A sisal covered scratching post or mat will save your furniture. Start out clipping nails now - getting a baby used to it will help a lot when the baby isn’t a baby anymore. And spay/neuter as soon as your vet will do it - especially if the kitten is male. Males that start spraying before they are neutered may not stop afterward, so no need to let problems develop. My experience with cats (and I have a lot!) is that younger cats tend to recover more quickly, both from the anesthetic and the surgery, than older cats.
Have fun!
Indeed. Further, my vet tells me that spaying females prior to their first heat (before about 6 months old) significantly decreases their chances of feline breast cancer.
If you have things around that are easily broken put them away for awhile. Kittens like to throw themselves around and will knock stuff off of tables and such. If you have a washer/dryer learn to never leave them open, and check that no kittens have entered before you turn them on. Also, I had two that would jump into the refrigerator when I opened the door. Check your window screens for kitten sized holes.
So where are you getting your kitten from? Have a name yet?
To add to what indecisive1 said, be sure to close the toilet lid, and watch out if the kitten is in the bathroom while you’re in there. We’ve had one almost jump into the drink more than once. Kittens are very bouncy.
Have fun with the little critter! I always think I want another one but then I remember the four once-were-kittens I already have.
Get those pictures in here already!