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.
Play Peek-a-boo
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.
Sing songs
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!