Three eggs at start:
When you begin the game, go all the way to the right until you find a machine. You will be warped up, and if you use the elevators you should ride to the second floor. Go as far to the left as possible until you reach another strange machine; ride it to the top of a tree. Once there you should find three eggs. Put them in the machine under the tree and they all will hatch.
Activate any item or machine:
Press L near any button or toy to activate it.
Once you have the eggs as teens or adults, use the red fruits near the warp machine on both males and females to make them want a mate. Do not worry -- the plants grow back. Eventually the female will lay an egg.
Never eat the plants and mushrooms near the second teleporter (second floor after teleporting) as they will poison you or make the creatures not want to mate, plus other effects. The other plants where you begin on the first floor where you begin are very helpful and safe.