Spraying is perfectly natural cat behaviour and their way of marking somewhere with information about themselves. That said, it's not particularly desirable if done in your living room!
Before trying to solve a spraying problem, it's important to determine your kitten is actually spraying, not just urinating. The latter is performed squatting, whilst spraying is carried out standing up. Small jets of urine are pumped out on to vertical surfaces.
What to do
Take your kitten to the vet to rule out Lower Urinary Tract Disease. This treatable, but potentially very serious condition could cause your kitten to urinate outside her litter tray and thus be confused with spraying.
Spraying is often the behaviour of a stressed cat. Consider recent events that could have upset your kitten. These could be 'big' things like the arrival of a new baby, another pet, or a house move, or 'little' things like furniture having been moved around in your kitten's favourite room.
What can you do to make your kitten feel happy and secure again?
Never punish a kitten for spraying. Cats do not understand punishment and, since spraying is often a result of stress, it can actually make the problem worse.
Cleaning the area that's been sprayed thoroughly is vital. This is because any lingering smell will only encourage your kitten to go and 'top it up!'
Many popular household cleaning substances aren't suitable, because they contain ammonia and chlorine. Both of these are found in cat's urine so can make spraying in the area again more tempting.
Instead, give soiled areas a wash with as dilute solution of biological washing powder. Rinse and allow to dry. Then, after testing for colour-fastness, spray with surgical spirit. Allow the area to dry before letting your kitten back in the room.
Castration of male cats can end spraying in 80% of cases, and in most cases this works immediately.
In the vast majority of cases, spraying indoors can be quickly and successfully dealt with. However, if the problems do continue, seek the advice of your vet who may prescribe drugs or a visit to a behaviour counsellor.