This is a labor-intensive job but very worthwhile, and I commend your interest. I suggest asking your child's classroom teacher for a conference for this specific purpose. You can ask the teacher for a copy of the alphabet with arrows indicating the proper formation of each letter. It is important that you get this because there are a variety of programs and you need to know exactly what the school is teaching so that you are consistent and reinforcing what the teacher has taught. At the conference ask for a sample of the paper being used (size between lines makes a difference) and a demonstration of correct pencil grip.
Now you have your work cut out for you. It is essential for you to watch your child form each letter -- children are very good at making letters incorrectly that look close to being right. Only the incorrect letters need to be practiced.
Once you have verified that each letter is being formed correctly, move into practicing words. Rather than writing the same words your child works with in school, try to pick words that are more meaningful. Some things to try: dictate a short grocery list; write a thank you note or invitation; tap into your child's interests and write letters to request information about a place your child wants to visit; write a letter to the governors of several states asking if they have pets; make lists of jobs to be done; the names of all the men or women in the family -- anything the child would be interested in without making it seem rote.
This is an excellent subject to help with at home -- it can be done in short amounts of time, and gets parents and children working together. And it's easy to see the results.