This mod isn't well-documented and it took me a bit to figure out how to start playing, so I'm jotting down a few notes for new players who find themselves in the same boat (badum-tish).
You will start out in a small area with three ships -- this is the game's lobby. However, you will not be able to access the subrooms of the ships until you depart. To get things going, click the "Crews" button at the top of the screen. Name your expedition, select the maximum crew size and click "Propose". This will make you captain, and if you're playing with other players they can join your crew at this time (Edit: by being on the ship when it departs). Click "Launch run" to launch the topmost docked ship. Make sure to get on before it leaves or the expedition will be aborted. (Edit: if players join the game mid-expedition, they'll spawn on the ship)
The ship will reappear next to an island and slowly approach the shoreline, creating a large red dock around itself once it runs aground. Now is a good time to acquaint yourself with the layout of the ship.
In the rear are two "Electric energy interfaces", which behave like accumulators but have an infinite charge, meaning you can indefinitely power up to 3.0 MW of machinery. (Edit: the infinite part seems to have applied when I was playing solo, but not in multiplayer games?)
Entering the car in the aft will take you to the Captain's Quarters, which contains chests for spawning quest rewards, a market building, and belts which consume items to accomplish various things. You can trade for artillery shells for your cannons, rail signals for navigating to other islands, uranium (I don't know if this has any special use), and the option to spend an extra minute at sea in between islands. Placing coal in the lower blue chest will add fuel to your ship. I haven't played long enough to find out what the other chests are for.
Leaving the cabin and entering the locomotive in the center of the ship will take you to the Ship's Hold. The hold contains a number of wooden chests that are unfortunately a permanent feature. The belts on the sides are connected to the belts on the upper deck of the ship, allowing transfer of items between z-levels. I don't know what the belts in the fore and aft are for (maybe you can upgrade to an additional hold later?). The substations flanking the locomotive are also connected to the substations on the upper deck, allowing power transfer between z-levels. A small pond at the fore allows the generation of steam and use of recipes requiring water. In all, this is an excellent place to build a long-term mini-factory, safe from biters. Note that solar panels don't work down here.
Returning to the upper deck, the pair of cars at the fore will take you to the Crow's Nest. This will give a simulated zoomed out view of the "world map", and has a pair of blue chests used for navigation. More on that later.
The last features of the upper deck include two blue chests on the bow used to fine-tune where you land on an island, and two artillery turrets, your "cannons". The game is over if a cannon is destroyed. You don't technically own them, so you will not receive any notification if they are attacked and they cannot be repaired with repair packs, so guard them carefully.
Now that we understand the layout of the ship, let's go ashore. You may notice there aren't any resource patches. A finite number of patches will spawn when you mine the boulders strewn across the island. In addition, you receive a small amount of money for mining boulders, trees, killing biters and destroying nests. Each island has a rocket silo, which will reward you with significant fuel and money in exchange for charging it with electricity. Some islands may also have a structure which grants a reward in exchange for a few hundred copies of a specific item.
Exploit the island for all the resources you can, keeping an eye on the resources lost fighting off the intensifying waves of biters. You can spend as much time as you like on the first island, although subsequent islands have a two hour time limit. The captain can choose to leave at any time by clicking the "Undock" button at the top. Anyone who doesn't get on the ship before it leaves will be marooned on the island and die.
The ship will spend a few minutes at sea, burning fuel until it encounters an island. If you go up to the Crow's Nest, you might notice the world map is split into three lanes. Buying 100 rail signals from the market and placing them in one of the blue chests in the Crow's Nest will make the ship change lanes, consuming the rail signals and bringing the ship to a different island. Once the ship arrives at an island, it will cease burning fuel and spend an additional minute at sea. You can buy additional idle time at the market, which you might spend researching technologies.
Once the ship enters the island's z-level, you can influence where it will land by placing rail signals in the blue chests at the bow. The ship will drift one tile port or starboard for each tile moved forward while a chest contains at least one rail signal, consuming a rail signal in the process.
Some other things to be aware of include the console commands. Bringing the console up with ~ and typing /help will give a list of commands. For the most part these are used to kick/ban players, to cheat, as well as to do player class related tasks. Typing /help <command> will give a description of a command. Leaving or disbanding your crew will discard all progress -- emptying your inventory and resetting the technology tree -- and kick you out to the lobby, so use that option with care. Finally, note that you get a research productivity bonus the further you've traveled into the game -- it might be worthwhile to hold off research until later to get the most out of your resources.