My first paper for the Harvard Extension course I'm taking in comparative education policy - I focused on the socio-economic inequalities in early childhood experiences that lead to differences in school readiness.
My Quora answer to "What are the most high leverage activities I can do with my 1-2 year old to promote his mental and cognitive development?" - http://www.quora.com/Child-Development/What-are-the-most-high-leverage-activities-I-can-do-with-my-1-2-year-old-to-promote-his-mental-and-cognitive-development/answer/Teresa-Gonczy
Good diet, rich & varied environment, and having fun are all very, very important! Overall, happy parents = happy baby, so if you're stressing out about promoting development, then it's not worth it. But that being said, there are specific things that you can do to promote baby & toddler mental and cognitive development...
-Talk with your baby. A lot! Describe everything that's going on - focus on the here and now so that your baby can connect the words you saying with the world that he can see and interact with.
-Make sure that you are using specific words, not pronouns (he, she, it, etc). For example, "Oh look, there's a dog. See the dog running. That's a pretty black dog. Oh, the dog is coming over here. Ha, the dog licked your nose!" will teach the word 'dog' much faster as opposed to "Oh look, there's a dog. It's running. Isn't it pretty? Oh, it's coming over here. Ha, it licked your nose!"
-Be sure to talk *with* your baby, not at your baby. Interaction is just as important, if not more important, than amount. Turn your speech into a conversation. Watch and listen to your baby for their responses - little coos, widened eyes, puckered lips, waving hands. Also when you aren't interacting directly with your baby, try to stay aware enough to still respond to these little cues. By giving attention to these 'language/conversation attempts' no matter how small, you're teaching your baby and your baby's brain that his noises and vocalizations are important - and then he will practice them more, and the more he practices verbal interaction, the better he will get!
-Learn some basic sign language and do the signs with your baby. Combining the physical movement with the lots of verbal language helps your baby to use multiple parts of his little brain. You didn't need to learn a lot of signs - in fact, it's often better if you don't because then it often helps parents (and thus babies) to really focus in on the most relevant concept in a string of words. Using the 'dog' example from above, if you combine it with doing the sign for 'dog', then the baby cues in more to that the word 'dog' refers to the fluffy thing running around, rather than any of the other words you said.
-Start practicing executive functioning games. Self-control and the ability to inhibit behavior is strongly correlated with success later in life. So start working on it now, but in a fun way. Play Opposite Simon Says where your toddler has to do the opposite of whatever Simon Says. For example, if you tap once, toddler should tap twice and vice versa. Or if you say 'dog' they point to the 'cat' and vice versa. (Obviously you do this after your baby has a very firm grasp on the correct or non-opposite way.)
-Make sure your baby gets enough sleep and downtime. Your baby's brain needs time to consolidate all of the input it's receiving. So baby needs sleep! :-) Also your baby needs some time to just take in the world, be able to self-regulate, etc - so you don't need to be interacting with your baby all of their waking hours either.
Hope that helps! :-) As another responder said, it's not worth hothousing your child, but there are some simple changes you can do in how you interact with your baby and what types of activities you do with your baby, which can have a huge effect on helping them to grow and develop mentally and emotionally.
My thoughts on education, cognitive science, early childhood, organization management, non-profits, and whatever else I happen to be thinking about! :-)