That is one of the main questions I had for my self when I started doing this. I have only been unschooling/homeschooling for five months, so I am just starting my homeschooling experience. I have noticed a difference in attitude with the my two girls and they seem happier, which is I believe just as important as their education. So how do I know, I interact with them daily and ask questions and they get the answers right and now if we don't know the answerer they suggest getting on the computer and looking it up.
I got into a discussion with my six year old about our bug problem, well she wanted to know if mommy roaches lay eggs or have them in their tummy. You know what I had no idea and was not sure if I cared (I just wanted them all gone) - so we looked it up.... then she decided she would do an art project and make them a house so they wouldn't want to live with us - this went on and on for hours and many animals were talked about and how those mommy had babies and what house would be best for them and their babies.
My eight year old looks stuff up on google and then tells me about it, or will ask me questions and then tell me about it days later. She is doing multiplication and is only in second grade she knows most of her states and capitals and can now read Dr. Seuss books with no problem. This was my child who they told me would need special help with reading because she was so behind and we (yes both of us) would cry every night because he homework was so hard.
So how do I know - just by watching, listening to them, if your get the chance do it - you will love it, enjoy it, and ask yourself why didn't I do this sooner.
What is your story - how do you know if your kids are learning anything?
