Ascent starts you off with some tutorial missions. You'll learn the ropes, like how to move your ship and how to navigate the map and stations. Eventually, you will reach a point where you'll need to earn some coin in order to advance. There are a couple ways to go about this. You can play taxi/delivery man and drop off passengers/packages. Or you can trade.
There are 8 primary star systems which you have access to without a Hyperdrive. Each one of these produces a resource, and buys the rest. There are 9 resources available for trade. Trade in these systems is primarily with NPC's, as you advance in the game you will get more into the player based economy. Normal trade rule applies: buy low, sell high. Below are what each station trades in.
Vestra - Aluminium
Sol Invictus - Carbon
Apollo - Meat
Veritas - Titanium
Vulcan - Iron
Ceres - Grain
Ubertas - Vegetables
Pamona - Fruit
There is not really any supply and demand factors at work in the Apollo (starter) sector. It's meant for new players, so there should always be a way for them to make money. You can often find profitable trades between systems right next to each other. I have a nice little trade route between Sol Invictus (Carbon) and Vestra (Aluminium).
My goal is currently to save up enough money to buy a Hyperdrive, which runs about 800,000 on the Galactic Market. It's not cheap, but it is certainly attainable. Getting to that point in the starter ship would be brutal. I've upgraded my ship twice already. I started out with a Ladybug (10 ton cargo), then bought a Sparrow (20 ton cargo). I recently purchased my third ship, a Unicorn, which has a 40 ton cargo bay.
So buy goods, take them to another system, sell them. Rinse and repeat. It's not the most exciting activity, but it goes pretty quick as travelling does not take very long and the interface is easy to use.
Next up, starting up my grain farm!