The first year is the fastest growth stage in a cat's life, and what a kitten eats during it affects its health for years. Kittens need more calories and protein per kilo than adult cats, in small, frequent meals. Here is what they need at each stage.
Birth to 4 weeks: milk only
Mother's milk is the ideal food. If the kitten is orphaned or not nursing, use a milk replacer made for kittens.

Do not give cow's milk, as it causes diarrhea in most cats.
First week: a feed roughly every 2 to 3 hours, day and night.
Serve the milk warm, with the kitten lying on its belly, not its back.
After each feed, gently rub the belly and bottom with a warm cotton pad to stimulate urination and bowel movements.

4 to 8 weeks: weaning

Start by mixing kitten wet food with milk replacer into a soft mash.
Gradually reduce the milk and increase the food over two to three weeks.
Place a shallow, clean water bowl nearby.
Meals: 4 to 5 small meals a day.

2 to 6 months: rapid growth

Kitten food only, as it is rich in protein, calcium and DHA to support growth, bones and brain development.
Meals: 3 to 4 a day.
Combine wet food (for hydration) with kitten dry food (for teeth and getting used to crunchy textures).
Follow the feeding table on the pack by age and weight.

6 to 12 months: getting ready for adulthood

Meals: 2 to 3 a day.
Keep feeding kitten food until about 12 months, then switch gradually to adult food.
If your kitten is neutered at this stage, watch its weight as calorie needs drop.

Do kittens need supplements?
If a kitten eats a complete and balanced kitten food, it usually does not need supplements. Kitten vitamin pastes can help weak kittens, poor eaters or during recovery, but it is best to ask your vet first.
Common mistakes to avoid

Giving cow's milk.
Feeding adult cat food before one year of age.
Changing food suddenly.
Too many treats (they should not exceed 10% of daily calories).

Products at Catu Store

Kitten milk replacer such as Pro Art kitten milk.
Kitten wet foods such as Felix Kitten, Josera Kitten and Reflex Plus Kitten.
Kitten vitamin pastes such as GimCat Kitten and Feline Go Kitten.

This article is for general information. Ask your vet for the right schedule for your kitten, especially for orphaned kittens.