These two words are very often confused. A typical mistake is when somebody uses "its" instead of "it's", although the opposite often happens, too. Actually, it's not very difficult to remember which is correct in a given situation:
you can only use it's if it is the short form of it is or it has (been). Here are some examples:
When you go abroad, it's a good idea to take a guidebook with you.
(... it is a good idea...)
Don't worry, it's been like this for a long time.
(... it has been like this...)
Are you telling me that it's my fault?
(... it is my fault?)
The box was hidden in an attic during the war and it's been there
(... it has been there...)
Its is a possessive word, just like my or your; it means that something owns something or something belongs to it. Examples:
The car was badly damaged but its driver escaped unhurt.
The dog went back to its house.
The house and its garden are a popular tourist attraction.