Cellblock Winning Strategy!
 

This strategy works best in the earlier tournaments (Tournaments prior to tournament 11). This method has been tested many times and it has been found that 9 out of 10 times, the user will win. Why will the user win? If you imagine a game of connect four, the best way to win is to set up a diagonal and horizontal line so that the last piece, will always bee on top of each other, so no matter where your opponent blocks, you will win either with the horizontal line, or the diagonal line. This method here sets up your pieces, so in the end, by step 9, you would have forced the opponent to place his block under step 10, and thus you are free to place your next block in step 10, to create a line of four, by which the opponent can only block one!

So what do I do in the instance the computer won't cooperate with me for one in ten of those instances?
englishladygodiva has provided us with the answer.

I was always concerned with the 10th time out of 10 where you had to totally abandon the strategy. By sheer accident, I discovered a way to ensure success should it happen.

Sometimes at the beginning of the game, the computer will block right next to (or near) move #1 instead of starting on the set of three that you block with move #3. To prevent this from messing up your plan, do not go ahead with move #3. Instead, place one piece all the way on the edge of the board, horizontal from move #5. The computer will block exactly to the left of move #5 after you have made it, leaving you free to complete the game as usual.

I've also found you can successfully eliminate move #8 and skip right to #9 without any problems.

Things to be aware of
Although the image shown above is what usually occurs in the game, there are always slight variations. For instance, sometimes steps four and five are not needed. As you play, do not mindlessly just add blocks here and there, be wary of where your opponent has placed his!