I have an old basketball injury concering my wrist. How do I keep from respraining it?

I tore some ligaments in the lower wrist of my shooting arm over a year ago. Since then, I have mildly sprained it at least a dozen times. It's re-torn when I picked up a textbook with one hand and carried grocery bags. When I rotate it, I experience mild to medium pain. I've played games through it, and it doesn't make the pain much, or at least noticeably, worse after. The sprain normally heals between 4-7 days. Nonetheless, it's a real pain. How can I minimize this injury's impact on my daily life?

to some degree, that wrist will always be weaker than the other one, because of previous injury. I suspect that you did not rehab the wrist or at least, enough rehab to fully heal it.
You should strengthen and stretch the wrist. Get 3-5 lbs. weights and do wrist flexion and wrist extension exercises against gravity. Also, stretch the wrist in all three planes, then add clockwise, and counter-clockwise.

Wear a brace, I'm a nurse. Schedule an appointment to get one or buy OTC.

Don't use it.

Ok, this may seem gross, but it works, trust me. Wrap your rist in raw steak, then, let it stay 4 about 3 hours. try not to get too wild with your games, but have fun, dont worry bout a stupid infection thing. it will heal up.

Problem is, once ligaments are stretched out of shape, they never go 100 % back without really intense physical therapy. Thats why people keep popping out shoulders after initial injuries. Like the nurse said, get a brace to support it. Strength training will also build up the muscles around the ligaments, tendons etc and make the joint stronger. (thats what PT does)
You can go see a orthopaedic surgeon. He may have options for you. If its bad enough, surgery may be an option. He may send you for PT and they'll give you exercises to build it up. You shouldn't let it get worse though. All these injuries will add up and you'll have problems with use when you get older.

a brace