Answer: There are hundreds of varieties of cactus and I'm not sure from your description what you have. Here are some good reference books with color pictures. Perhaps your local library has them, or can borrow them from their lending system.
This website has photos of cactus, listed by Latin name: http://eebweb.arizona.edu/herb/plantphotos.html
Also, the following site from the Smithsonian has botanical drawings of cactus. Perhaps one of these will help you identify your plant. Good luck!
As for care, most cactus don?t tolerate freezing temperatures. If you have freeze warnings protect the plant by wrapping it in burlap, or put white styrofoam cups on the growing tips of tall, columnar-type cactus as protection, sort of like snow hats.
Cactus don?t like to sit in wet soil. They rot if there?s too much moisture and they must have excellent drainage. Most indoor container cactus die from overwatering. If possible, buy a soil mix especially for cactus or have your nursery order some. Or, use a mix of 1 part potting soil to 2 parts sharp sand, and 2 parts perlite or pumice. Most cactus like plenty of sun, but some need partial shade from hot afternoon rays, so it would be great to identify exactly what you have.
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