I have struggled to really find a method that would help my active three year old learn preschool topics. I think he wasn't ready for some of the things I was trying to do with him, and my method wasn't meshing with his hands-on learning style. I really didn't want to force him or make it seem like a chore. I wanted him to start learning and have a good experience from the very beginning.
I month or so ago I found out about Tot trays. I lay out 5 trays every day on the counter with different learning activities about letters, numbers, handwriting practice, cutting, sorting, and other topics. It really has been a success so far. He calls him his "juegos" (games). He gets to choose which activity to do and how long to do it. He loves having a choice and usually does them all in one day. I switch one or two out every day to add variety.
The activities pictured above can be found here:
(I made the printable, but got the idea on the website)