So you want to attach a fucking petpetpet to your petpet on your active pet?
1. Get a petpetpet!
Right now Veespa's are cheap as shit (30k~) so stock up while the price is low and hoard them like the jew you are for resale in the future.
2. Fill your inventory with other junk as well just in case some random event happens and destroys/steals your shit.
3. Choose the pet that you want to have the petpetpet attached to. Make sure your pet has a petpet first, otherwise it won't work, dumbass.
4. Go to your inventory and refresh for a while.