There are two main ways of traveling around the Galaxy. The first, and cheapest, is your own ships propulsion. You can travel to any system within range, and must then buy fuel to travel onwards from there.
When you warp to a system like this, you may meet other ships along route. Police, pirates, traders and passenger liners all frequent various systems depending on the type of system it is. Most ships will ignore you, but pirates will attack you and police may sometimes inspect your cargo hold for illegal goods.
How you interact with each encounter is up to you, and is part of the way you define your place in the Astral Sea.
The second way to travel is through Portalling. This is a service provided by the Hi Tech worlds that enable you, for a price, to jump across the Galaxy. This price is dependent on both the size of your ship and the distance you have to travel, but is a great way to jump around if you ever get stuck or you desire to be elsewhere.
When you arrive at your destination, you are presented with the services that the Dock offers. Here you can refuel, repair your hull strength, and restock on food for your crew to eat. Crew who aren't your Captain or First Mate will require payment upon docking and will slowly grow unhappy if you choose to not pay them.
The Docks also offer banking services for loans and a hospital (that may differ in quality and cost depending on the planet you land at) in case you require medical help your doctor can't provide.
I can't help but notice that Lowry is at an industrial age level...I take it the Prime Directive doesn't apply to this universe?
Correct! Think Firefly more than Star Trek; hi tech planets mixed with lower tech colonies or worlds that have decided to do things differently. Everyone is aware and welcoming of space travel, but the worlds themselves are at differing levels of development.
Next week I'll go through Trading.