Synthesis in organic is perhaps one of the hardest type of problems for most students to tackle. There are two main components that are needed when solving synthesis problems: 1) a vast knowledge of reactions and 2) critical thinking and analysis. These two facets of problem solving make synthesis questions difficult for many. So, you may be asking, how one would methodically tackle synthesis problems.
The first step is of course to make sure you have a good understanding of the reagents needed to make various transformations. You can think of reagents as tools in a tool belt. If you hired a carpenter but his tool belt was empty, what could he or she build? One suggestion that I have is to create a log book of some sort to keep all of the reactions together. You can add examples of various reactions as well. Look for a later post that contains reactions!
The next thing you need to do when working through a synthesis problem is to work backwards. You need to find logical areas on the molecule that allows you to connect two pieces. This is often referred to as a "restrosynthetic analysis" and is an extremely helpful technique. Working backwards in such a fashion helps break down a complex molecule or problem into something simpler. See the video below for an example.
Good Luck!