Your answer is really going to depend on your ds' school policy and school culture. Do you know any other parents who volunteer? If you do, ask them how they went about volunteering - who did they ask, how did they ask, what types of volunteer work are they doing.
Has your ds' teacher asked parents to help out in the classroom (or outside of class?). If so, have you volunteered to do one of those jobs - that is most likely going to be the easiest and quickest way to get "inside".
Next thing to do is to look for ways to get to know your ds' teacher better so that she isn't just seeing you as a parent helicoptering. Start simply by just focusing on saying hi to her or offering up some simple chitchat about the weather or whatever if you see her at drop-off and pick-up. Don't make every connection with her be a question about what's happening in the classroom or what's up with your ds etc. Does the class go on field trips or have class events where parents participate? Definitely join in on those - drive on a field trip if you can, it's a great way to get to know some of the other kids in class and to see how your ds is relating to his classmates.
If your teacher hasn't specifically asked for any type of volunteer help, is there something you can think of that would possibly help both the teacher and class? One thing that our elementary school teachers were usually open to was when a parent wanted to help with support during times like writer's workshop or reading groups etc. I used to help my ds' first grade teacher by coming in one morning each week and giving individual oral sight word and spelling tests to the children. I never worked directly with my ds - I wasn't allowed to. But that was ok - I had a chance to see where the other kids were at, my ds saw me helping, and my work helped cement a good relationship with ds' teacher so that I felt comfortable asking for differentiation for him and she was open to listening to my requests. Later on, when my ds was struggling with written expression in early elementary, I volunteered to be a parent assistant during writer's workshop - I never really helped my ds directly because he didn't want me to help, but it gave me a wonderful opportunity to see the work of his peers which helped me understand better where ds was at - plus it was fun
Another friend was concerned about math differentiation, so she approached her ds' elementary teacher with an offer to spend one day per week during "math hour" teaching challenging math to the top-math students in the class. Another place that our schools have appreciated parent help is during class library time - helping kids pick out books, reading to the kids, just helping maintain chaos. The teachers usually *aren't* in the library with the kids, so you're essentially helping the librarian, but it's a type of help that the teachers appreciate, and it's a way for you to get to know the other children.
So think outside the box a little bit - is there any kind of thing you can think up where you can help the classroom as a whole or help the teacher in a way that she would appreciate? Something that lets the teacher know you are sincere in wanting to help for more than just a day here or there? Something to give you an edge up on credibility that your wish is to help, and that lets you into the classroom. Most teachers I know through my friendships do not like parents "observing" but they appreciate help.
Hope that helps a bit!
polarbear
ps - what types of things is your ds complaining about? I might be able to come up with something more specific if I knew what issues were of a concern. I'm sorry I don't remember specifically! pb