Many people ask this question. You have some good answers above. Here are some more.
Set up the colony when the mice are under breeding age. 4 or 5 weeks old. Use one male and 3 or 4 females depending on the size of the container. Remember at some point the cage needs to hold the parents and 40 or 50 babies. Once the colony is set up, NEVER change it. Don’t take anyone out and don’t add anyone new.
Multiple males will fight. They will bite each other’s testicles and render each other useless for breeding purposes. If you take a male out of the colony and then try to put them back, often the females will not take him back and will kill him.
Once set up, be patient. With young mice, they may not breed for a few weeks. Then there will be a three week pregnancy. Don’t be surprised if the first batch of babies takes a month or more.
First time mom’s often eat their babies or fail to raise the whole group. Expect it and don’t get upset if it happens. Cannibal mice are most often a sign of a problem in the set up. Stress is the number one cause. Too much traffic by the cage, noise, constant checking by you, are all stress factors. Inadequate diet or insufficient food, lack of water. Over crowding. Too hot. After you have eliminated all the problems that might have been caused by you, then you can decide that it is a problem with the mouse itself and get rid of the offenders. It is easier to start over than to deal with a problem colony.
Mice don’t deal well with heat. Try to keep the temperature below 75* F.
Lab blocks are the best most balanced food you can use. If those are not available, use a mixture of grains and low fat dog or cat food. Do not use table scraps. Go light on raw vegetables. Never feed any kind of lettus. This will give them terminal runs. Water should be available at all times.
I typed this in a hurry, sorry if it is a little disjointed.