Encouraging children to do home work is challenging, particularly if they're fairly young. Particularly for a good student, homework is often boring in my experience; for many students, repetition is an effective way to learn, particularly repeating the same thing at different times. For students who learn quickly (like myself, and my son), that sort of repetition is flat-out boring. And even for students who don't learn as quickly, it's hard to see the long-term benefits.
For us, what's worked is making homework a habit, or rather a set of habits. My son's in second grade, so a bit younger, but I suspect this applies at a fairly wide age range. Homework is something that's done before games, and while that was a small struggle, it didn't take all that long for him to come to accept it as a fact; Tuesday he came home, for example, and said, "Dad, if I do a load of laundry and do my math homework can I play my video game?" That's pretty easy to say "yes" to. He doesn't see it as being forced, but just as one of the things to do.
That incentive structure is one that works well for my son, and I suspect will work well for many. Sure, it starts with complaints, and it's probably not as ideal as him choosing to do it on his own for his own reasons - but for my son, at least, external incentives are very powerful. As he grows older, the incentives will need to grow with him; right now it's a "now" incentive - do your homework for the day/week and get some video gaming time - but as he grows older, longer-term incentives may work better (particularly if he becomes challenged in an area).
We also are careful to make sure to give him a say in the rules. He largely has an amount of homework that must be done by the end of the week - not just "do this tuesday do this Wednesday" - and so we allow him to manage how that's done, so long as it's done, with the understanding that if it's not done then his Thursday will be a lot. We help him think through the consequences of putting it all off, particularly as Tuesday is the easiest day to do homework due to our pickup arrangements; but sometimes he does put it off, and that's fine - so long as it's done, and he accepts the responsibility when his Thursday is a bit boring.
If your child is finding homework boring, then one other thing you should consider is talking to the teacher. My son's teacher gave him a workbook at the start of the year, knowing that he was 2-3 grades ahead in math, and told him to work on that instead of the regular sheets of math homework - do a page or so a day of that instead. We're lucky to have a teacher who does that proactively, but other teachers might well be willing to do so if you approach them. Homework should be individualized for the student, and should be appropriate for what they need, with particular goals in mind - and while it's not necessarily practical for a public school teacher to give 30 different homework assignments, that doesn't mean you can't get involved and make sure your child has the right kind of homework. Good teachers can find the right balance, in particular by not being overly repetitive, and by helping their students see why the homework is important.
As far as to what age you should be involved, the answer is probably older than you think. This article at The Conversation titled "Here's what you need to know about homework and how to help your child discusses a study (which unfortunately succumbed to link rot and I can't find) that shows that the benefits from parental involvement seen in lower-achieving students in elementary school seem to disappear in secondary school as parents become less involved - suggesting that more involvement could help, even at that age.
However, the kind of involvement matters; this study by Cooper, Lindsay, and Nye shows that positive parental involvement - not well defined in the abstract, but I interpret it as meaning actively helping with homework - is associated with worse outcomes, while supporting the child's autonomy (which I interpret to mean providing space and time to do homework, but not actively interfering with it) is associated with better outcomes, at all grade levels - and positive interference was worse particularly at lower grade levels. I'm not sure how well they controlled for ability, but it's a good reminder that at any level it's not the result of the homework that matters nearly as much as the journey. I would caution taking these studies with a grain of salt, also; they’re very inconsistent in how they define things and in what they find.