Step1.) show you will be responsible by cleaning up and doing all chores needed without complaining
Step2.) learn more about the pet you want how their behavior is, what diet they need, what environment the require and any other details depending on the pet.
Step3.) Remember it is an animal and they all have feelings just like us so make sure its gonna be a pet that will always have u happy and that you will always take care of. Absolutely no excuses otherwise your parents may get upset when u don’t attend to your pet when its ur job to take care of them.
Step4.) if you can try saving up some money it will show your parents you really want to have a pet but also once u gain knowledge upon the pet you want tell them all the facts you know to them.