What do I do after
If you used way 1 or way 3, you will also receive a map with the route to the slavers' hideout. But you should not go there immediately. You need to return to the New Ark slums and visit the tattoo saloon. There you need to make the same tattoo on your face as the slavers have. They will first apply this tattoo to the other cheek, so you need to use the "mirror" option. The color of the tattoo is dark red. Then go back to Sunshine and buy a headwrap in one of the shops.
With a tattoo on your face and a headwrap, you can go to the slavers' hideout and bluff the guard at the entrance (do not try to sneak past him).
If you used way 2, you will have to do the same, but you do not have a map yet, so you will need to visit the slaver in Sunshine first - go through the hidden northeastern passage and show him the tattoo. He will relax and you can just take the map. After this, you can immediately go to the slavers' hideout.