There's nothing you have to do.
If you want to breed nephelym, you need to build barns to hold each type: the builder, Cassie, can be found in the Hedon Township, and it costs money to build each barn. You can earn some money from the alraune Fern on your farm up to I think a 100 times each time you let her blow you, which come to think of it might be the only real way to get money until you have at least one barn to hold nephelym you capture.
The Lustwood is only the place with wild nephelym open to you at the start, so you'll want to build barns for Vulwargs and Foxen first, as those are the two types of wild nephelym in the Lustwood. To capture a wild nephelym, go up to one, click and initiate surprise sex. You have to click rapidly (use use the cheat code in the menu "win surprise sex" to auto-win) to keep your orgasm bar from filling before the nephelym's bar does. If you orgasm first, you lose Lust and the wild nephelym merely walks away. If they orgasm first, you have the option to capture her, and she's sent automatically to your barn.
But you have to have the right barn first to capture one.
Lust, the orange meter at the top left, is your sexual energy, each sexual encounter drains some. Winning surprise sex will refill your Lust some though, and sleeping to start a new day will refill it completely.
Once you have some wild nephelym captured, go to the breeding area and pair them off (with each other or with your breeder), to get them pregnant. There's a Breeding Requests board that has requests for specific nephelym that you can try to fill for money if you want, or just ignore it (like I do).
To unlock other areas of the world, you have to find blessed nephelym (the unique ones that talk) and fulfill their requests in order to obtain their keystone to open gates. Once they tell you in conversation what they want (a specific wild nephelym with a specific gender, trait, and level), their request will appear on the Breeding Requests Board in the Special Requests tab. Once you have what they want, turn it in at that tab, then go talk to the blessed nephelym so she thanks you and offers you the keystone, then pick up the keystone from next to her, then open the gate.
There's also a keystone you can get in the Hedon Township. After you fuck Cassie (the builder), new dialogue opens where you can ask you about a lever. She'll say she repaired it, so you can run up the stairs and follow the rooftop path to the end (past the mermaid) to the lever and throw it. This opens the gate near the temple's entrance by the stair's, which lets you get into the dungeon and fuck the slime girl, who then lets you take her keystone.
