The laws of kashrut require that in addition to not eating them together, we wait a specified period of time between eating meat and eating dairy.
After eating dairy and before eating meat, eat something pareve (neither meat nor dairy) which does not stick to the palate. Then rinse your mouth, or take a drink, and wash your hands. In addition, many have the custom of waiting a certain period of time—a half hour or an hour. After eating certain hard cheeses, a six-hour waiting period is required.
After eating meat foods, we wait six hours before eating any dairyAfter eating meat foods, we wait six full hours before eating any dairy. If even the smallest amount of food is chewed or swallowed, the full waiting period becomes necessary.
If food is tasted but immediately eliminated from the mouth before chewing or swallowing, then no waiting period is required. One should, however, rinse the mouth well.
Meat and dairy foods may not be eaten at the same meal, even if they are in separate dishes and even if the waiting time elapses.
There are also certain slight restrictions on eating meat together with fish, and in certain communities, on eating fish together with dairy. Click here for more on this subject.