How to predict the products of a organic chemical reaction
You need to build a working knowledge of known reaction mechanisms that include the functional groups of your reactants. Put another way, (1) identify the functional groups present in your reactants and (2) check known reaction mechanisms that proceed by reaction of these functional groups. 

Really, the only way to be good at this is to study and memorize organic reactions. There's a number of resources to help with this (e.g. online flashcards, and I really like Chemistry by Design, an app that you can use on a smartphone).