I'm not sure I fully understand your question. If you want to know what is going on in the school and to monitor your child's progress, then volunteer. Schools are always looking for good people to help out.
If you can do it during school hours that's great. I would volunteer in your child's classroom if possible. That way you can observer how your child learns and interacts with others. You will also get to know the teacher, and she will be more likely to keep you informally informed.
If you are unable to volunteer, then request regular conferences (formal and informal) with your child's teacher. They can be emails, phone calls, notes home or face-to-face. Most teachers like to have concerned parents who want to help their child. Listen to what the teacher has to say. If they offer suggestions on things you can do at home, then follow through with your child.
If you'd like to give me more information about your question, I might be able to offer some more suggestions.