It's perfectly reasonable to ask for some advice, especially as vets are not open 24/7, and it's impossible to force everyone to try and pay for an emergency call first day a kitten gets home (students own cats too, and if someone says poor people should just not own animals, I'll get mad).

That said. Yes, the kitten needs a vet, but before you can get one (it's the weekend too, not good timing), some more questions need to be asked. You got this kitten straight from an owner, meaning she was bred, not sold as a pet, correct? If she is not pedigree, then you should be aware that 'free' kittens can often cost more than an adopted shelter kitten.

Regardless of the outcome from her vomiting tonight, you need to take her to the vet's ASAP for vaccinations (her first round should be had soon), and desexing if she needs it (she's in fact too young to be alone in a new environment, 12 weeks + first vax would have been best, +1 week for desexing and recovery). Without the vaccinations, she may die of a preventable illness if she is let out at all (and quite possibly if she isn't and some other animal visits her).

Kittens have very sensitive stomachs, and can regurgitate things they don't like as well, ask the previous owner what brand of food she was being fed, what type/hardness and what size the pellets were. If your kitten shows foaming when she throws up, it may suggest she is in some kind of respiratory trouble (something stuck down her throat). Provide her with fresh water (not tap if you live in a hard water area), and see if she is able to have any.

Look around her area/room to see if there is any chance she ate something else that she shouldn't. There are many toxic houseplants, household chemicals, human food items and so forth that cats are fatally 'allergic' to.

Do NOT feed her milk or ice cream. Do not pick her up right now except to put her in a pen where she cannot damage the floor (put down something for her to lie on that's soft/comfortable, but washable). If she is also having loose stools, then you must get her to a vet ASAP, no two ways about it. See how she is in the morning otherwise, and if she is not meowing in pain and does not seem tender when you touch her (if you touch her tummy and she yowls at you, you know she's in massive pain), then she might recover on her own and you should ask for the exact type of food she accepts.

Do take her to the vet at first opportunity for check up, vaccinations, desexing and microchip registration. It will cost around $250 to $400 for the courses of Vaccinations and other involved costs. She should be kept warm, indoors and dry. Put down more food in the morning only after you've confirmed what she can eat.

Okay. Why are you on yahoo answers? Shouldn't you be taking her to the vet? People like you are lazy and usless at taking care of animals.