Before you think I'm a tiger mom, who forces her kid to do worksheets and flashcards, we do a LOT of learning through play, which is what should be done when teaching a toddler.
One fun activity that DD loves is stickers. I pick up stickers whenever I'm out shopping. I can usually find them for 99 cents or a couple dollars, depending on the size and amount of stickers. I have to keep a lot in stock, because she can easily go through 50 stickers in one sitting. The best places I've found are Dollar Tree, Walmart, and Party City.
DD has small notebooks that we call her "sticker book". She puts her stickers in there. She also has a jumbo coloring book that she enjoys sticking stickers in as well. It came with HUGE dog stickers.
Things she learns when doing stickers:
names of things
sounds animals make (if we have animal stickers)
fine motor skills (peeling the stickers off)
So much more!
When doing stickers you can ask lots of questions about the sticker, and they kid doesn't even know they are doing "school". It's an inexpensive way to have fun and to learn.