This guide assumes a lot of things. The things you must have/have done before listening to me are -
The Free Worlds Campaign
The first half of the Wanderer Campaign (until/after the Eye opens). Make sure that you are not doing a mission involving you fighting a fleet. These missions will make it impossible to capture ships and bring them back to a planet. I suggest taking a pause after completing three of the four after-Eye Wanderer missions to amass a fleet, because the battle following those missions is not pretty without quite a few T2 warships.
A jump drive (although not technically necessary, I personally find it to not be an option.)
At least 800 fuel. This is what I have, but I also have a pretty powerful ramscoop system, so you might need much more than that

There are also some recommended things. I have captured some ships without these, but these make it so much easier.
A cloaking device or ship with inbuilt cloaking (Some Remnant)
A strong anti-missile, at least a Point Defense Turret or two Wanderer anti-missiles
A ramscoop. Depending on the amount of fuel you have, this may or may not qualify as a must have
A ship with a whole lot of defensive value. Ideally, this would be one of the big ships (Bactrian, Carrier, or Dreadnought) but really any heavy warship can do. If you don't have this (example - Remnant Starling), you better have speedy engines and a cloak.
A place to store fighters or drones. I personally have never captured a fighter or drone, and I don't have the docks/bays for them either on my Dreadnought. If you want to capture them, though, you won't be able to bring them out-of-system without some docks and bays.
Sunbeams. If a puny ship is trailing you, rather than cloaking, you can blast it and try to capture it.

This is a pretty big list, but it should all fall in naturally if you play along the beaten path of the game. Some of this stuff is a bit of a splurge, but when you're capturing ships worth 22 million at 25% of their original value, it'll all be worth it.

At this point, if you checked all the mandatory prerequisites, you should be able to land on the new Wanderer planet in Korath territory. Kaliptari, the system in question, actually plays a surprisingly minor role in the heat of things. What I find it useful for is storing the ships. As you can see from the picture, I have escorts stationed there. This system is my personal preference for keeping my captured ships.
The highlighted route is not a coincidence. The system Mesuket is the prime place for hunting, or really, boarding Kor Automata. The Korath from both factions literally fight each other to the disablement here. That's right, disablement, not death. It's like they give the ships to you.
Once you enter that system, cloak immediately if you have one. Then run up to a corner of the map, so nothing is visible away from the edge of the minimap. If there are no Automata in the system, you're in luck. If there are, cloak and flee or just run until they lose interest. Once ships from the other faction get there, they will ignore you.

This is the part that takes the least amount of effort, but the highest amount of skill. The two factions will brawl it out, for some reason always fighting to disable. Make sure to uncloak. Stay in the corner between one half and two minutes. Then, circle around the current fight. If there isn't one (you should be able to see in the minimap) wait a bit longer until the two factions come head-to-head.
Don't worry about resources being exhausted. More and more reinforcements for both sides always seem to come.
Once they are fighting each other, circle around the current fights, looking for disabled ships. The areas where they fight are very dynamic, and ships tend to leave after disabling their enemies. If you wait a while, there will be large swaths of unattended, disabled ships.
Wait for nearby fleets to go fight somewhere else, then disable your cloak and spam board on every ship you find. A general rule of thumb - The bigger the ship, the more likely it's going to blow you up. Of course, this applies if the ship wasn't disabled, but it also applies if it is. Bigger ships are more likely to blow up on attempted boarding/capturing. Their explosion radius is also significantly bigger, and the explosions are much more damaging.
If you manage to successfully board one, I suggest only taking weapons if you have extra cargo space. The ship needs everything else to escape to safety if you successfully capture it, and the weapons are usually the most high-value things the ships have anyway.
After you board and pillage it, it's time to attempt to capture. Capture success chances are directly proportional to the ship's board success chances, so it's very hard to reliably capture ships like the Kar Ik Vot 349 or the Model 512.
If you fail to capture, scram. If enemy ships are after you, shake them off, shoot them, or cloak. The ship will self-destruct, so if you stay still you will die.
May RNGesus have mercy on you.

Before I figured out this trick, I lost many a great Automata ship. But now that I know it, I can share my knowledge with you.
The second you capture a ship, scram. It is very unlikely that, if your ship is disabled or destroyed, this opportunity will present itself again. For the larger ships, you only have a 4% average capture success rate.
But do not scram to Kaliptari. If you do, there's a sizeable chance you will get blown to bits by the Kor Mereti.
Instead, scram too...
Ka'ch'chari, in OG Wanderer space.
It doesn't matter that the Automata ship can't follow you. Go here, land, and save your progress, risk free. Then go back and land in Kaliptari. As long as your new ship is not disabled, you now have a surefire way to get it to Kaliptari without getting blown up. If you are, just reload your save, and everything will still be there for a second try.
Once you land on Spera Anatrusk, park your new ship. Congratulations, you now are one step closer to absolutely wrecking everyone with no added crew cost.

If you have extra outfits (ex. Jump Drives from Korath raids in Remnant space), equipping them on your Kor Automata ships is a great way to store them. Just make sure they have enough space. You might have to clear out some weapons or ammo racks.
I have experienced personally that ~35 Kor Automata ships, not including fighters and drones, are enough to complete the Wanderer storyline without losing a single ship.
The Kar Ik Vot 349 or the Model 512 are great flagships. Soup them up with Wanderer gear (much more lightweight), then head over to Kor Efreti space and grab a Command Center and a few Bunks. Even without the automata, the flagships are several times more powerful than any ship in human space.
If you want to get closer to a powerful ship sitting in the middle of a battlefield, cloak and go up to it by boarding it. Then, once you are literally on top of it, uncloak and board it. You can steal from it, but I wouldn't recommend capturing because there's a high chance that ship will be disabled. Recloak if things don't go your way.
To be able to board Kor Mereti after pacifying them, zap one on the edge of the system by selecting it and firing. You do not need to disable it or even do real damage to it, just send a laser at it for half a second. Immediately cloak, then wait for the ship to go back to fighting the Kor Sestor. Fair warning - Until you leave the system, the Kor Mereti will be hostile to you. Given how preoccupied they are, this shouldn't make too much of a difference.