I was wondering how u get trait points? Like, if I want to generate a new pet.

you need to obtain a generator essence- guide here

If you actually want to make a pet, as opposed to just create a design and save it to create at a later time, you need an essence of the species you want to create first. There are three types:
. Regular (2 Trait points)
. Enhanced (4 Trait points)
. Mystical (4 Trait points)

You can get essences by buying them from another player, buying them from the diamond shop (Note: this currency costs real money), or, very rarely, from (1) defeating enemies while exploring, (2) doing a run through one of the dungeons, and (3) nurturing pets in your or other players hatcheries.

This is a good guide about all the above: https://www.sylestia.com/forums/?thread=51639.