Just like humans, cats have 2 sets of teeth. The first set is called the milk teeth or deciduous teeth and they start to come in when the kitten is about 4 weeks old. They continue to come in until all 26 milk teeth have appeared, usually by 6 weeks. These teeth are non-permanent and they begin to fall out from 11 weeks until 30 weeks.
This is a time which is similar to teething in human babies, so the kitten may have sore gums, may do a bit of complaining and may eat less due to pain. During the time when the milk teeth are falling out, new permanent teeth are coming in until all 30 of them have developed and have replaced the milk teeth usually by 8-9 months.
When a kitten matures a bit:
After six months, it is a good idea to start getting it used to regular brushings. Some cats are more prone to tartar build-up and gum disease than others. The most important thing to remember about brusing a cat's teeth is to not use regular human toothpaste, some of the ingredients are toxic to cats.
You will find appropriate toothbrushes and toothpastes intended only for cats at your local pet shop or veterinarian.