Yes, they certainly do, with their own rules that have to be learned like the rules of other languages. Due to the ways sign languages are used, there are some key differences in the rules, especially about word order.

In American Sign Language (ASL) for example, the general order for a declarative sentence is known as 'topic followed by comment'. However, the topic isn't quite the same as the subject which would normally begin, say, an English sentence; it could also be the object. Topic could be defined as 'the main thing we are talking about'. The time at which something happened is usually (not always) given at the start of a sentence, and there are agreed signs for pronouns like I, you, your etc. A lot of small 'grammar words' aren't signed, so you could have a sentence like 'I teacher', rather than 'I am a teacher'. In practice, though, people often follow a word order similar to that of English when signing.