Use the adjective exacting to describe something or someone very precise or strict in its requirements. If your teacher has exacting standards about spelling and punctuation, you better carefully check your final paper.
An exacting person expects things to be, well, exact. For this reason, demanding is a good synonym. Friends who are exacting might let you have it if you show up a minute or two late. Some exacting people are extremely selective about what they eat, rejecting anything that doesn't meet their complicated standards of nutrition and taste.