1. Focus on what's important. To really live simply, you need to know what is most important in your life and then to focus on that. In homeschooling, I have a few basic goals for my kids and I try to stay focused on those. One of our goals is for the kids to have a strong grounding in Scripture. To that end, we do Bible study almost every day.
2. Eliminate educational "clutter". Clutter is the stuff around us that we don't need or use. One big source of clutter in education is busywork. Kids in school do lots of busywork, but kids educated at home can be more focused in their work. If a child understands a math concept, there is no need for them to do three more pages of problems. Instead, they can move on to applying the concept and come back for a review in a few weeks. (This is one reason we love ALEKS. The kids move on to a new concept when they have shown that they understand the current one. The program reviews every few weeks to make sure they don't forget what they learned.)
3. Stick with what works. In our family, we have found that Sonlight works really well for us. It is the absolute best curriculum? I really don't know. We're happy with Sonlight, so I haven't gone looking at other curricula. To this end, I rarely look through homeschool catalogs unless I need something. There is always the temptation to think that the resources on the page must be better than what we're using now. Overbuying curricula wastes time, money, and bookshelf space. Of course, when something isn't working, then it is time to get something different. We don't stick with a bad resource just because we paid money for it.
4. More is not always better. This is true in a myriad of ways when it comes to home education. There is no need to purchase every book that my child might read when the library has them anyway. If we change from one curriculum to another, I don't keep the original curriculum cluttering up my shelves. There are tons of books published every year on many different subjects. My kids will still grow up to be well-educated even if we don't own, or if they don't read, every one of those books.
5. Accept educational gaps. Not everyone can learn everything - and trying to make them will just make everyone crazy. Mr. Math Tutor and I know the basics of what we want our children to learn before they leave home but it doesn't include everything that they could possibly learn. If a child isn't going into a science-related field, there is no need to push for them to learn calculus. Not every child needs to know the details of art history, or how to build a solar panel. Once the basics are covered, we encourage our children to follow their interests. (Remember, kids coming out of institutional schools don't know it all, either.)
6. Combine subjects. Particularly in high school, students can combine work in more than one subject. Ga'hoole Girl writes about what she is learning in science or history which gives her practice in writing (mechanics and composition) while helping her synthesize the ideas from the other subjects.
7. Make everyday life at home part of "school". This comes naturally in our home, but I include it here as a reminder that normal life can be included as part of school for record-keeping and making transcripts. Ga'hoole Girl is learning food science this year while doing a lot of cooking (along with reading about the food and writing critiques of her cooking). Things like sewing, home decorating, and car maintenance can all be included under the heading of "school".
8. Practice contentment. This is a broad category that encompasses many of the previous points. Unfortunately, discontent is rampant among homeschoolers. As parents, we worry that our kids aren't learning enough, that we didn't choose the right curriculum, or that we spent too much money. The Bible's admonitions for contentment, though, apply in homeschooling as much as anywhere else. Philipplians 4:19 reminds us that God will meet all of our needs while 1 Timothy 6:6 tells us that "godliness with contentment is great gain." And, my favorite - 1 Peter 5:7 "Cast all your anxiety on him because he care for you."
I certainly have not succeeded yet in making our family's educational venture as simple as I would like. I have found, though, that the recommendations I have listed are a good start on the road to "Simple Schooling".