whatwillibe, welcome to TCS. Caspar, kitten accidents aren't inevitable at all. If you follow a good method, you'll have great success.
When you bring your kitten home, you'll need to confine her to one or two rooms for the first 24 hours or so. This helps her adjust to her new home. Visit her as often as you can while she's confined. Make sure she has her food, toys, bed and litter box in the room with her. Keep the litter box and the food separated as far as possible as cats don't like to eat near their litter box. She will soon learn where it is and once she's used it a few times, you can let her out into the rest of the house. Take her to the litter box every few hours during the first day she has access to the whole house and let her find her way back by herself. Don't move the litter box around, otherwise she may not know where it is. Friends and family who have taken my kittens follow this method and none of the kittens have had 'accidents'.