Cats are naturally very clean animals, so toilet training is generally quite easy with new kittens. You will need to invest in a good quality litter tray, ideally with low sides that are easy to access for little kitten legs.
If you know what litter the kitten has used prior to adoption, it is recommended to use the same litter initially. This will make toilet training a lot easier to begin with. If you are not sure, that is ok, there are lots of different litters to choose from.
When you first bring your kitten home, keep them isolated to one room initially. This will give them time to adjust to the change in environment and learn to use the litter tray. Place a feliway diffuser in the room to help them feel calm in their new surroundings.
Place them in the litter tray and, gently using their paw, encourage them to scratch around. This will give them an idea of what do in the litter box. You can place them in the tray several times a day, after playing, eating or sleeping, to encourage them to use it at times that they typically need to toilet. Once they have perfected the litter tray in this room, then allow access to the rest of the house.
Place the litter tray in a central location where the kitten spends a lot of time, so that they have easy access to the tray. You should have multiple trays for the different areas of the house, especially important in multi-story houses, as this will minimise the likelihood of accidents happening. As your kitten grows, less litter trays will be required.
It is important to remember that kittens are still learning and accidents may still occur. In the event of an accident, do not reprimand your kitten. Clean the area up quickly using an enzyme-based cleaner, to ensure that the area is thoroughly cleaned and there is no residual smell. This will decrease the likelihood of your kitten urinating in the same area again.
As previously mentioned, cats are extremely clean animals. For this reason, it is important to clean and change the litter tray regularly. If the litter tray is not clean, then your kitten will be less likely to want to use it, and will be more likely to have accidents in other areas of the house.