I know how to get project pets and how to design an end goal, but how do you actually start a project? Do you just start breeding once you have the space or what?

You basically just get the starting pets for the project, cross your fingers, and start breeding them. Hope this helps (lol)

You'll find that everyone has there own way of setting up and running a breeding project. You'll probably have to play around a bit to see what works for you. A couple of things you'll want to keep in mind:

1) Naming - how are you going to name your pets in order to keep track of who can breed with who. Some people also use the names to keep track of traits. I tried that initially, but it didn't work well for me (especially when I was tired). So, I pick a letter for a project that all the pets will be named with and then use a notebook to keep track of traits and parents.

2) How many pets are you going to keep - When I first started a project I was really bad about releasing pets and they quickly started to over run my stable space. Now I pick one tab per project and that forces me to prune more. Some people only keep the best two or three males, while I keep five (they fit nicely along the bottom of the project stable tab). That way I don't have to be quite as careful about who can breed with who and with projects that have a lot of traits, I can have a variety of vis and carried to breed with my females.

Once you decide on the above, it's just a matter of breeding, keeping the best and releasing those that either didn't get the traits you wanted or are being replaced with those with better traits.

Hope that helps!