As a former preschool teacher, I am a huge advocate of learning through play. By doing what they enjoy, children naturally explore, discover, and learn about the world. I view the pre-school years as the time not to do school, but instead to develop the skills that will lead them to a lifetime of school success. Skills like large and small motor skills, thinking and problem solving skills, creativity, curiosity, and most importantly, a love of learning; all of which they can learn naturally through play and everyday experiences. However, that doesn't mean that you shouldn't provide specific "learning activities" that can direct their play towards learning some of those skills. I am currently trying to put together a collection of such activities, to pull out every day for Benjamin that he can do at the table while I am doing dishes or starting dinner (or just sitting with him!).
These are simple activities that I made to help develop fine motor skills, hand-eye coordination, and that can also be adapted to teach other skills, like sorting or counting, but in a fun, play-based way.
I found in my cupboard a couple of small cans of coffee beans that were past their expiration date. I tossed the beans but saved the cans and covered them with cute paper. I used a hole punch on one lid to make several holes, then cut pipe cleaners into small lengths that would easily fit in the can. I showed Benjamin how to put the pipe cleaners through the holes, which he happily continued doing. When he was done, we dumped them out and started over! Use what you have: you could just as easily use a small box, and use something like cotton swabs or toothpicks instead of pipe cleaners.
On the other one, I cut a slit for coins. Same sort of idea, but using a different object turns it into a new and exciting activity for a toddler! Try other objects, like buttons, beans, or almost any small item. Obviously, these activities need to be closely supervised as they could be choking hazards. You could adapt this for an even younger child by using a large coffee can with a larger hole for blocks, small balls, etc.
These can be further adapted to encourage skills like color recognition, sorting, etc. Use the following ideas or your own! For the pipe cleaner can, color around each hole with a different color. Encourage them to put each pipe cleaner through the matching color hole. If you have several cans, you could label each with a number and encourage your child to put that many objects in each can. Or, make two slits on a lid, a small one and a big one and give them different sized buttons to sort through the different holes.
A final note: with young children, the focus for these activities isn't necessarily for them to do it "the right way", but rather for them to explore and have fun - and they're bound to learn something during the process, even if they get creative and do the activity differently than you've planned! =)