I feel like everything now is pretty well addressed in the FAQs page, under pets, which I'm going to go ahead and add to this thread for easy reference. If you take a peek there and still can't find what you might be looking for let me know!
You can get a steamwork pet three different ways!
You can create a new pet (you pick a name and Isaac will hold on to it while your pet is being built) which will result in the steamwork icon gender, this will require you to have a slot open for when the pet is complete.
You can have a current pet changed into one, you pick a pet to transform (so you will already have the pet in a slot).
or
I hope that helped!