The best thing my mother did was break the monotony of study. We went to every single museum we could find. We went on adventures when she went to sell stuff on military bases. She would spend one extra day at the site taking us to anything of historical interest or cultural signifigance. She let the world be our classroom. Nowadays, if there is a subject you cannot help the child with personally, try joining the online tutor programmes available. I think one is called etutor or something. People with special skills join up as tutors, and you use the service to meet with them, and they get with you to discuss pricing. Then they will tutor your child on the subject they are skilled with. I joined up for help to one a while back, but I can't find the dang link anymore. At any rate, check out the online tutoring services, because they do work, especially with math!

I am currently homeschooling a child aged 9, 14, and 16. I had been homeshcooling for about 8 years, and my style has changed considerable since I started. I started off very concienciously trying hard to do the "right " thing. I realized I was working so hard because of outside pressures of feeling judged, and being worried of buying into other people's fears that I was ruining my kids if I homeschooled them. I followed a Waldorf curriculum, which I like a lot. But I only did things with my older kids till end of grade 6, and then I backed off and let them go their own way.
I read and loved A.S. Neil's "Summerhil" . what I took from his book was his belief in children, and that it made sense to allow them to become selfmotivated rather than motivated to please me because they need my love, or out of fear. it's all about trust.

Each child is different, so I find that it makes sense to follow your instincts and allow the child to lead.
I think in our society too much is made of being "busy". We as adults don't let ourselves take breaks without it being officially being called a vacation, and we often freak out when we see our teenagers loaf around. But I think even when on the outside not much is going on, change is being processed on the inside. i don't think it's bad for them to have space to allow things to move at their own pace, even when it is not ours.
One of my favorite author's on teenagers is a waldorf teacher called Eugene Shwartz he said there is no such thing as teenage rebellion, but only adults who have not dealt with their teenage issues. I can see in my own life with my kids that this is true.