[Works on Mobile] Click the breeding structure, then click two monsters. Wait for the monster you bred. Click on it once it has bred then wait for it in the nursery. Once it's done in the nursery, click on it and you have a new monster! Then you can start breeding all over again until you have them all. You need 3 monsters to unlock the Mammott. You need 7 monsters to unlock the Potbelly. You need 19 monsters to unlock the Wubbox. You need 20 monsters to unlock the shop. For breeding and nursery, the timer needs to count up to 100 for it to be done. All monsters take the same time. Monsters will take half as long to incubate/breed after waking up the Wubbox. When you power up the Wubbox you can breed all your monsters back. The Wubbox will take all monsters except Noggin, Toe Jammer, G'Joob, Shugabush, Ghazt, and Punkleton. There is a 100% chance for a epic monster and a 0% chance for rares and commons! The only common var If you breed a monster while you already have one, you can click the breeding structure again to confirm or click away to cancel breeding. Once the shop opens, you can select monsters to buy as eggs or placed directly onto the island. Some monsters may require you to wait a certain amount of time until they are fully activated on the island. You can hover or hold your finger over a monster to see how much time it has left. The only common and rare varients it has are the Dipsters, Wubbox and Rare Wubbox, Werdos, and Shugabush.
Thanks to @mysinginmonsters for the original game! If you want, I would follow him and check out his studio for other island simulators!