Mostly trial and error. He was hard to place for math because I had never really given him much at home, so he wasn't as advanced in math as he was in everything else.
When we started homeschooling, I gave him the Singapore Math placement tests to see what level to start him at. (I had heard good things about the program for GT kids, and I wanted something that didn't require the computer.) Well, he was teaching himself how to do the problems from the tests! First time he'd ever seen the material, I'm sure of it! So did that count as having gotten the questions right?

Very confusing!
I more or less threw a dart at a level and chose one. He whipped through a couple of years of Singapore in a couple/3 months. Then we hit the times table wall. He knew how to multiply, understood the concepts very thoroughly, but he was not ready to memorize the times tables at age 6. It was very low-concept, high arithmetic. He was not liking math at all. So we skipped anything that required more than casual use of multiplication. But even Singapore--as good as it is--does a huge chunk of 2-digit multiplication in one book, then 3-digit in the next, then 4-digit in the next. Ugh! By the 4-digit book, we were skipping most of the book, and it didn't seem worth it anymore. He didn't love math, and the work just wasn't hitting him where he lived, you know?
So I decided to go "off road." I found a great (library) book by Lynette Long called "Painless Geometry" that offers simplified but not "dumbed down" high school geometry, and we used it to finish out the last 2 or 3 months of last year.
He LOVED it! It appealed to his visual and highly logical nature. It required high-concept thinking but little arithmetic. It was challenging. It was something new every day.
Bliss! He blossomed!
This year, I wanted to work on the times tables, but timed tests didn't work, so we did a lot of strategy math games with dice and cards and finding patterns in the times table. It started sticking. To reinforce the multiplication and continue the geometry we did the previous year, we started working with shapes and fractions. Pattern blocks were a big hit for this. When he breezed through that, we started doing fractions on paper, which upped the multiplication requirements.
He's currently in a math class for 9-12yos and is one of the top performers. And happily, he just totally loves math. Even when plenty of arithmetic is required.
The moral of this (long) story: I found that if I crank the conceptual challenge level up high enough and keep his strengths in mind as I do so, he's motivated to do the arithmetic. He's learned his times tables by osmosis, he loves math, and he's doing pre-algebra with ease all of a sudden.
Math is more than arithmetic. When I focused on finding conceptual challenges for him and let the arithmetic take care of itself for a while, he learned it.
Did any of that answer your question, IronMom?