Chess thought process

I've been playing chess for a while off and on.  As of late I am trying in earnest to be a better player. 

I have the Chessbase "The basics of winning Chess by Andrew Martin".  I really enjoy watching him as he dissects a game from the masters and explains where things work (or don't).  In some parts he tells you to pause the lesson and see if you can figure out the next move.  This is where I have the problem.

I can't seem to pick out the best move.  A move that doesn't seem to make sense falls into place later in the game.  When I'm watching him explain the moves everything seems so simple as he walks you through the game.  When I'm playing against the computer I can't seem to think many moves ahead in the game.  A small plan but a lot of the moves are reactive.  I'm positive I miss many opportunities to mate for this reason.   

What is the best way to practice to help in this area?  I'm sure this may be second nature to some but I really have an uphill battle with this.  

Thanks all.