Children have one set of 20 teeth, which are called the baby teeth or primary teeth.

Typically, baby teeth begin to come in around the age of six to ten months. From this age up through about three years old, most children will continue cutting teeth until they have the full set.
Primary teeth usually come in beginning on the bottom in the center, and then working backwards, followed by the top center, also working backwards. Typically the primary teeth have all appeared by the time the child reaches three years of age. However, the answer to how many teeth children have is not always exactly 20, depending on various circumstances, but in completely typical conditions there should be 20 total primary teeth.
The primary teeth stay in place for just a few years. Around age five or six, the child will probably begin to lose his or her baby teeth, so the number of teeth children have will change.
Permanent teeth grow in during the same time frame that primary teeth come out, with one gradually replacing the other until no baby teeth are left and all permanent teeth are in. By age 12 or 13, the child will typically have their adult teeth, totaling 28 in number.
Interestingly, the full set of adult teeth actually includes 32 total. These include the premolars and wisdom teeth, the last of which tend to come forth around the age of 20. Not everyone develops wisdom teeth; this depends on the size of their jaw, heredity, and various other factors.