First you need to hire marines. Fill your ship full, the Elite can fit 3 and you.
Now go and explore. Fly around and use the long range scanner to ping stations. Although most free ships I found are near gates/highway entries.
Non owned ships are easy to spot on the map as they have no faction call sign. The Peregrine on the picture was only name "Peregrin Vanguard" instead of the usual "TEL Peregrin Vanguard" or others.
Once there beware of the mines. They are always around abandoned ships. Sometimes a few sometimes more. They have a yellow glow. Try to put yourself and the neutral ship in a position where the background is dark ideally black, they are easily visible that way.
Stay 1-2 Km away from the ship with the mines and start pocking at the mines from that distance. If the ships shield drops it will show up on the hud, normally it has no indicators above unless targeted. If this happens wait a bit it will recharge, haven't found a mine field yet that completely took out the shields of a ship if I took it slow.
Once the mines cleared select the ship, press F and chose claim. A small marine pod will launch towards the ship. Sometimes they bug out and orbit the target you can send another in this case and kill the loser.

Now pray that the marine doesn't blow up all the systems on capture.. It will sadly happen.
You can find small ships this way as well. Marines can't board those. You'll have to board those in the space suit after hacking.
TIP:When selling captured ships for profitssssss, first enter the upgrade screen and set the automatic upgrade slide to the minimum. This will strip everything from the ship including consumables.
Sometimes these ships come with a hella lot of laser turrets/satellites. I've got 2 million out of a pirate Kestrel this way where I forced the pilot to bail, simply selling it would have been a 1,5 million loss.
Found an Ospray, 2 Vultures, 3 Magnolias, 1 Elite and this Peregrin this way.
This was near the Eigtheen Billion Gate of Memory of Profit IX. However I think these ships are procedural.

Bonus: I've unlocked a Teladi start, not sure when it happened.
