How does the asl grammar structure work?

Grammar in ASL is pretty simple and flexible. Here are some basic rules.
1. Place the subject of the sentence first. (STORE ME GO)
2. When you’re using a negative, place it at the end of the sentence. (ME EAT EGGS NOT)
3. Don’t use the sign for because. Use a rhetorical question instead.
“I’m going to the store because we need milk.” would be translated like this: ME GO STORE WHY? MILK WE NEED
4. Learn how to use classifiers. They are very important. They help to make ASL true ASL and separate it from SEE.
5. Don’t forget to use proper non-manual cues. Head nodding, neg, eyebrows raised, eyebrows down, etc. (makes you seem more deaf)

Hope that helps some. There is a really good book out there for linguistics of ASL that helps you to understand sentence structure and grammar a little bit better. It’s called: Linguistics of American Sign Language: An Introduction by Clerc Books, Gallaudet University Press, Washington DC.