Each sector has about eight space stations, of several different types as listed in the manual.  Three are special:
a. Every sector has a Trading Post, which sells some basic goods (at a high price) and also has a few other things you need;
          1. The Tactical Navigation system
          2. Singularity Engine (speed enhancer)
          3. Cargo bay extensions
You can also save your game here (Insurance)
b. Some sectors have a Space Equipment Dock, which sells weapons and armor.
c. Even fewer sectors have a Shipyard, which is where you go to buy your own space stations.  More on this later.
The others all buy one or more resources and sell one product. They also sell "Insurance" (i.e., let you to save your game).  Do it.
So find a station selling something you can afford, then take it to another station that will buy it from you.  Buy low, sell high.
Nothing to it!