You can encourage your toddler's cognitive development simply by playing with him. Plus, it's pretty nice for you too. Whatever you do, let him know that you're proud of him, and that it's okay to make mistakes.
Read aloud every day.
Even for 5 or 10 minutes. He's learning words by hearing you say them. Name objects in the books and let him point to them.
Explain things as they're happening.
Make it a conversation, and listen when he talks.
He truly believes he's invisible when he holds his hands over his eyes. How fun is that?
Ask him to find things.
You'll be surprised how much he knows.
Expand on his words.
If he says “car,” make it into a sentence.
Put faces to voices.
When friends and family call on the phone, put pictures near the phone so he can see who's talking to him.
Play toddler learning games such as “Name The Body Parts.”
Play with blocks.
An excellent study in cause-and-effect.
Introduce new environments.
New playgrounds. The grocery store. The children's room at the library.
Experiment with chunky crayons.
Help him color on paper with them, and learn NOT to eat them!
Give him choices.
But not too many!