How can I become a better Connect Four player?
Connect 4 is a solved game.  Memorize the solution, and you should be able to win every single time.

Go to the following resource

http://www.connectfour.net/Files/connect4.pdf

I came to that link from The Wikipedia article, so in case the link ever breaks, you should be able to find another by searching for the "connect 4 solution"

That article has a lot of strategic analysis about connect 4, and Even if you can't memorize the solved strategy perfectly, you should be able to glean a lot of good strategic practices from section 3 which is titled Some Strategic Rules for Connect-Four