Complete the formal writing using whatever language comes natural to you. This means that your formal writing could include contractions for certain words and leave them out in other areas. For now, don't pay attention to when you use contractions. Just write naturally.
Go back through your writing to make sure you have used the contractions properly. Contractions are used when two words are combined to make one, such as "it" and "is" combing to form "it's." Notice that the removed letter is replaced by an apostrophe.
Be aware of common mistakes. You should always be able to replace a contraction with the two words it represents. For example, in the sentence "The dog scratches its head," you cannot replace "its" with "it is" or "it has." Therefore, it is not a contraction. Proper use of the contraction "they're" is also a common mistake. You should be able to replace this contraction with "they are."
Read the formal writing aloud replacing each contraction with the two words being replaced. If it sounds natural to use the two words rather than the contraction, use the two words instead. However, if it sounds awkward to say the two words, you can use the contraction in the formal writing.