Families choose to homeschool for all sorts of different reasons.
We homeschool mostly because we want to be with our son and enjoy his childhood with him. He went to a Waldorf school for Kindergarten - 2nd grade. There were many things we liked about this particular school, but the full-day schedule was too much time away from us, so in 3rd grade we decided to make the jump into homeschooling.  It was the best decision we could have made.

At first I was really worried about teaching the subjects that are difficult for me (like math).
But now, one of the things I love the most is that I get to relearn all these things that I hated learning in school, but now can learn in a fun way!  We're all learning and making our son's education a space for discovering the world together.

Once we started, I realized everything we had been missing out on by sending our son to regular school. If you're thinking of making the jump and feeling nervous about it, do some trial weekends before pulling your child out of school. Take a Saturday to try it out. Plan some activities - make sure to include a subject that is difficult for you, and that you have to do some research for - that way you get a better idea of what you're in for.

Different homeschoolers do it in different ways.
I've heard of families that do it all in One-Hour-A-Day homeschooling. We do around 6 hours a day of academic work, plus another 2 or so hours of art and/or sport. I also spend around 15-30 minutes every night planning classes for the next day, and throughout our first year I probably put in a good 300 hours of research. Some working parents homeschool their children at night or on the weekends. Some families buy a packaged curriculum, others (like us) make up their own curriculum. There's no ONE right way. Try out different ways until you find the way that's right for your family.

It took me around 6 months to feel like I really had a handle on things. 
I think the most important thing, when you start, is to remember to keep it happy. Let yourself and your kid(s) fall in love with it.

You'll soon realize that there is no time pressure, on the contrary, you have more than enough time to do what needs to get done. Enjoy the beginning, it is the foundation for the edification of what will be your homeschool structure (or lack of one, if that works better) - maybe style is a better word.

For me, homeschool is also a political choice.
I want to see the world change radically, and hope for equally radical changes in the way we educate ourselves and our children.