Here are the explainer videos I mentioned... one is a 12-minute step-by-step guide and another is an hour-long clip from my stream where I show you how it works (and doesn't work) in practice.

Here's the short version: (12 minutes)

Here's the long version: (1 hour and 12 minutes)

Find a ship that is in fixable condition and in your price range.

You shouldn’t bother if you don’t have at least $500,000 in the bank. The smallest ships will go for about $200-500k. Luxury ships, even if they’re small and in bad condition, will sell for up to a million. Nuclear-capable medium-sized ships will range in price from $800k to north of $1 million. Large nuclear freighters and luxury liners will cost between $2 to $3 million.

By “fixable condition” I mean that you need to be able to get it spaceworthy enough to limp back to K LEG with it.

For that you need:
1. A working Nav computer
2. A battery with at least some charge
3. An RCS input like a Kang or Miura with at least one N2 can that isn’t empty
4. At least one working thruster

Bonus points if you also have an undamaged transponder and a working antenna, which means the cops won’t pull you over for flying dark.

Note that you should not use the transponder from your original ship and – if you try uninstalling it – there’s an 80% chance you’ll break it anyway. Using the wrong transponder on your ship is also illegal.

Take a PASS shuttle back to K Leg and head over to the Commercial station to buy the new vessel. While you’re here, take the opportunity to stock up on things like food, water or hull patches. Also go to the bathroom… because it could be a while before you get back.

If you don’t have enough money, this is where you give up on your ship-flipping dreams and head back. You’ll be a thousand or so dollars poorer, but you can pat yourself on the back for not being a save-scummer. Then you should strip that ship down to the studs to show those SOB’s at Ayotimiwa who’s boss.

If you do have enough money, you should make the purchase from the ship vendor kiosk. Once you do that, you can also purchase a new transponder for $23,200 and put it in your inventory drag slot. You can indeed take dragged inventory with you on PASS shuttles, which will make your life a lot easier.

You can also do this with a dolly. So, for instance, if all you need to get the derelict fully spaceworthy is a Thruster, a Transponder, a full N2 can and an Antenna, then you can easily fit all of those into a dolly with room to spare.

In my case, all I needed was a Nav Computer. Note that you CAN’T fit a Nav Computer into a dolly.
I recommend stashing a cache of essential equipment like Nav Computers, Thrusters, Kangs and Batteries in OKLG for this reason. Once you graduate to a large ship, you can keep this stash in your vessel at all times for easy flipping.

UPDATE (12-9-24): Cirne did some testing and digging in the code to get a lot more precise info about how ship pricing works. It's... not necessarily ideal and very abusable.

The pricing appears to be as follows:
Combined value of each item of equipment installed on the ship * 80% * Room specialization multiplier * condition (>33% = 25%; 33%-66% = 50%; 66%-95% = 75%; >=95% = 100%) * 300% oxygen bonus for having at least one o2 can with pump installed

Any walls - or anything that is installed with a center-point inside a wall - counts for ABSOLUTELY NOTHING. This includes pumps, thrusters, coolers and any floors/conduits.

There is NO LONGER a bonus for having many rooms on a ship. The most ideal layout for any ship is 1 Luxury Quarters, 1 Towing Room and everything else in a Reactor Room.

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So it used to be that you could reduce the price of a derelict ship before buying it by stripping out the valuable equipment, uninstalling all the doors and punching a hole in the hull.

This was never intended behavior. I know because I got into an argument with Joshu – one of the Ostranauts devs – who insisted that this isn’t how it worked until I showed him that it did.
Evidently they patched that, so now every derelict gets assigned a buying price when they’re spawned which does not change.

Once you buy it, the selling price is calculated with a formula based on the combined price of all of the ship’s components together modified by multipliers based on these factors:

1) The number of rooms, meaning enclosed compartments separated by walls and a door.

2) The average condition of all the ships components[ostranauts.wiki.gg], including the repair levels of the floors, walls and conduits. If the components are “luxury” brands like Van Hummel floors, that may impact the “condition” as well – but I can’t say for sure.

3) Whether or not the ship is capable of holding atmosphere. Meaning it’s a lot more valuable if it’s full of breathable air and there are no gaping holes in the hull.

4) The distance from OKLG. Meaning that you’ll get your best price if you manage to drag it back into dock.

On top of that, specific rooms have multipliers of the value of all the objects inside[ostranauts.wiki.gg]. For instance, a rec room or wellness room has a multiplier of 1.9 while an engineering room has a multiplier of 1.4 and a cargo room has a multiplier of 1.2.

Notably, NONE of the non-installed equipment or items on the ship count for anything, so be sure to sell everything you don’t want that isn’t nailed down at the License store before you sell the ship.
In full transparency: I don’t know what the equation is and I couldn’t find anyone on the Discord who could tell me confidently. I found direct answers from months and years ago, but they’re definitely out of date.

Once you’ve taken a PASS shuttle back to your derelict, you should get it at least barely spaceworthy – meaning Nav Computer, Battery, RCS Intake and Thruster – and then drag it back to K-LEG.
Ideally, you should use your main ship to tow it back as close as possible to K-LEG first using a towing brace.
What you want to do is point your main ship towards K-LEG and get around 20km away, then equalize your speed so that you’re in a relatively stable orbit around Ganymed. If anything, you want to be pushing maybe a meter per second away, so you don’t risk falling into the asteroid after hours of repairs.
If you haven't seen a towing brace:
The towing brace is actually very easy to miss. It comes attached to a derelict's exterior airlock and, when you uninstall it, it comes out in two parts. As of the last couple patches, you can also find it on sale at the Scrap kiosk in Port Azikiwe.
Installing it on your ship is a bit of a pain because you'll likely need to scrap or uninstall a couple of the corner walls and do some finagling to make it fit into your airlock.
Even worse: the sides of the towing brace don’t count as walls for keeping atmo in, so you’ll need to make sure there are walls on either side of the spots where you had to knock walls out.
Once you have it, you can lock onto a ship by manually unspool the tow cables in a long, slow animation... and then, in order to release docking clamps... you need to do the same long animation to release it.
Moving your ship with another attached without a tow cable causes massive damage to your ship. I did some modest boosting once to keep a ship from crashing into Ganymed and it wiped out half the hit points on almost all my walls/floors. With the tow cables, there appears to be no damage at all even with a good amount of boost, except for maybe a little wear on the airlock.
Here's an actual convo I had on the Blue Bottle Discord last year:

DUUD: "I thought you [couldn’t] tow without a brace?"

Magpie: "You'll break your ship and the derelict. But you can, yes."

ME: "Yeah like I said, I boosted about 100 mps total and ended up nuking half the hit points throughout my hull."

Since I’ve already told you what factors influence the price, the path now should be pretty straightforward.

First, you’ll want to hit auto-task and systematically repair every inch of the vessel, including all the walls, floors and conduits. You will probably have to uninstall a section of wall so you can go outside to repair all the bits and bobs you can’t reach inside. You might even have to uninstall things like Nav Computers so you can reach any nooks and crannies they keep you from reaching otherwise.

Then you’re going to want to install as many doors as humanly possible on the ship to maximize the number of specialty rooms, trying to install as much equipment as you can to reach the thresholds that are on the wiki to have the rooms counted for their specialties.

Keep in mind that, for instance, a cargo room isn’t a cargo room unless it’s minimum 6 squares on one side and has at least 6 bins or racks. Also, a bedroom doesn’t count as quarters if it isn’t minimum 8 squares on one side and DOESN’T have a toilet, IC reactor or canister.

Go to the scrap store to buy, repair and install any equipment that doesn’t clash with a specialty, because – with the multipliers – it’s practically guaranteed to increase the value of the derelict by more than you paid for it.

Once you’ve sold the ship at the trading kiosk, all you have to do is take one more PASS shuttle back to your ship, which has hopefully stayed safely in orbit a quick nitrogen burst away from the station.

Things to keep in mind:
A) While doing your initial investigation and repairs, at least one of your two ships must be broadcasting a transponder code (i.e. be sucking power) or the cops will board you as soon as you undock. If you undock while flying the NEW ship, then you will gltich out and possibly brick your save (you can see this happen to me in my long video).

B) Note that - as of the most recent tests - turning off your devices does not make them draw any less battery, so don't count on your main ship batteries to last while you're gone. If you're concerned about battery life, you should use a switch or uninstall a conduit to shut down ALL power on your ship.