You start with a sector of unidentified signals that may be planets, asteroids, or empty space. From the center, you drag the mouse and launch probes to start revealing signals.

When you uncover planets, you can see what type they are (Earth-like, jungle, artic, desert, etc.) and decide whether to colonize them. When you colonize a planet, it will have certain goods that it needs and others that it produces. Then you draw trade routes (slipways) from one colonized planet to another, so that one planet ships its products to another planet that needs them.

Sometimes, when you colonize a planet, there won't be other nearby planets that supply its needs or demand its goods. Which means you can't effectively integrate that planet into your trade network. You happiness rating will take a hit and you make less money. If you go bankrupt or let your happiness fall too low, the council kicks you out and it's game over. But if you play right, you can build a crazy-big trade empire.

About that council: it has five alien races, each of which offers its own perks and techs for the tech tree. You can choose three of them to accompany you in the mission. You can do tasks for them (such as exploring a certain part of the sector or producing a certain amount of a good) to get bonus resources and boost your score.
To advance up the tech tree, you have to build labs and supply them with workers and goods. This is difficult and pricey, but necessary, because the techs do all sorts of things from making your planets more productive to breaking the rules on how slipways connect. You're going to have to break some rules to stay in the game.
A game in Standard mode lasts for 25 years, and most actions take one to three months, so on average you're playing a 50-turn game. If you score high enough, you unlock the Ranked Run mode in which you play a different map each week to put your score on the leaderboard.
You can also unlock the Campaign, my favorite feature of the game. The Campaign is a set of 13 missions with a story called "Fate of the Forebears." The story is about anomalous rifts that are popping up in the galaxy and an ancient race that mysteriously disappeared long ago. This is familiar ground, and you only get a couple of sentences of plot before and after each mission. But each mission has its own unique objectives and gameplay twists, and each of the five council races eventually gets its chance to shine. Even when I aborted a mission because of a lousy start, or I played a mission to the end only to fail the objectives, I didn't feel discouraged because I was enjoying the campaign so much.
Another great feature is the Undo. You can undo a practically unlimited number of turns. So if you try to set up a series of trade routes but it ends up not working out as planned, you can undo the whole mess and try something different. But you can't undo a probe launch; once you discover new planets with a probe launch, you can't undo that or any earlier turns.
There were a couple of problems that made me bounce off the game initially: the icons and the tutorials The icons that show a planet's needed and produced goods are pretty small and somewhat hard to distinguish. I couldn't find a way to improve their visibility to my liking, but I grew accustomed to them. The tutorials tell you what you need to know, but they're noninteractive and too much to absorb all at once. I did the dumb thing and watched all the tutorials before playing the game for the first time. The smart thing would have been to watch a few tutorials, then play the game until I understood those concepts, then watch a few more tutorials, and so on.
Slipways is addictive, deep but accessible, and plenty challenging even on Reasonable difficulty (the second easiest of the four difficulty levels). If you're a 4X fan, I don't think Slipways will replace your favorite 4X game, but it will complement it nicely as a shorter, simpler alternative.