Kittens are typically weaned at between 7 and 10 weeks of age. The usual advice is to start them on water soaked dry food because dry food is less expensive. There is a huge problem with that, however!
Cats are obligate carnivores, which means that all of the nutrients that are necessary for their health are found in meat. Not only that, their systems do not deal well with nutrients found in plants. This is, in large part, why so many cats are overweight, diabetic, and have kidney and liver problems.Dry food has a great deal of carbohydrates which kittens/cats cannot digest and is actually harmful to them. Plus, cats instinctually get the majority of their water from their food, which they cannot do with dry food.
Kittens need a higher level of protein and fat than adult cats in order for proper growth to take place. So, whatever type of food you choose to go with, be sure it is designed for kittens. Once the kitten is a year old, it is safe to switch to an adult food.
Since kittens are obligate carnivores, canned food is the ideal type of food for them. However, you should research carefully to be sure you are feeding a brand that has high levels of protein and low levels if carbohydrates. Many canned foods contain high levels of carbs which your kitten will not be able to properly digest and will negatively impact their health in the years to come. Ironically, one of the best balanced foods (at least some flavors of it) is Sophisticat and Fancy Feast, which are relatively inexpensive brands. The food should not have more than 5 g of carbs per serving! A side benefit of feeding a low carb food is that your kitten/cat will use more of the food, thus producing less litter waste for you to dispose of!
Kittens will typically eat much more than adult cats because they are growing and active. It is best to offer them food 3 or 4 times per day, and most kittens will not eat more than it takes to fill them up. If you work and are away from home during the day, it is better to give a high protein/low carb dry food during your hours away so that your kitten does not have to go all day without food!
Beware of making your own food for kitten also. Cats require specific nutrients, including taurine and other vitamins, that you will not be able to put into homemade food. This causes major health problems over the long haul.
In addition, feed no more than the equivalent of one or two days worth of fish based canned food per week. There are unsafe levels of mercury in the fish that will not be good for your kitten.
It is a good idea to stick with one brand, but vary the flavors of the food for your kitten so that they don't become overly finicky eaters. Beware though, different flavors of the same brand can have different nutritional values!