Mother of four...
I generally only help if asked. That would include the teacher asking me to check over or sign off in some way. I'm happy to quiz a child on spelling words or help with a homework problem, whatever.
I do not, typically, check over work to see if it's been done properly. This is for two reasons: 1) teachers sometimes use different methods than I'm used to, to arrive at an answer. My "help" might add to the confusion; and 2) If my child isn't understanding a concept, the teacher can see that by looking at the homework.
That said, my kids are more inclined to come to me with math questions, rather than their dad. It's just easier for me--I remember much more of algebra. I also do biology and chemistry, and leave physics to him. I get English, he gets history.
The only other thing I'll say to the OP is, right now, you're setting the tone of the kind of help you'll give. If you sit down and go over every problem, it will become the expectation that you're going to do that every night. I've personally cases of parents doing their kids work for them--even, in one case, of a parent going to the school to present a project. I've had teachers tell me, "I can tell it was Child's own work." This is meant as a compliment!
