How I Use It
Art of Problem Solving is great as a problem bank especially for interesting non-standardized problems. The books actually work best for this. You can take sections out and enhance many topics. It might be useful for advanced learners but only if they're fairly self-sufficient.
I wanted to clarify the misconceptions in several of the previous reviews. Art of Problem is first and foremost a textbook and online class company. The website is meant as an adjunct resource for these purposes. So while there are several online tools like Alcumus on the site. These were never meant to be stand-alone.
Secondly, the primary focus of all the textbooks is problem solving. AoPS offers an extremely rich/deep take on traditional topics. The problem organization in the books is particularly brilliant with problems building on each other towards a more complex view of each topic. The style of questions is structured around interesting samples from contest math with a focus on rigorous proofs and building techniques for attacking harder problems. I highly recommend reading a sample chapter of the books and judging the material for yourself.
The books take a very constructionist approach with the students being asked to first try to solve a group of exercises and then explanations are given and structure is built up. For a few of the books i..e Algebra/Pre-Algebra there are companion videos which I've found useful. The overall level is geared towards advanced students. In practice, many kids find the jump from other texts to AoPS to be difficult initially because of the added depth and rigor. I can't imagine as someone previously suggested using any of this as a remedial program.
Instead, either you should the website as an additional resource if you're using the AoPS textbooks or it also works well as an enrichment resource with another curriculum. I'd suggest interleaving some of the material as appropriate and particularly as challenge problems within the normal sequence.