I want to get fillers injected throughout my face. Under eyes, cheeks and nasalabial folds. How do I know the plastic surgeon will be good?

Reputation. I think this is a time to say reputation precedes the name. Ask around, ask how many procedures they have done and how many are satisfied and best if you can ask someone or some people around.
Fillers. Have your face evaluated by a board certified surgeon with expertise in injections.
Surgeons expertise. Recommendations from colleagues and consultation with physician are usually your best guide to choosing a plastic surgeon. During your consultation you will likely see some pre and post photos and that should be able to give you an idea of your physicians expertise. Unless you have had significant weight loss, generally speaking a 23 year old is unlikely to need all the areas mentioned, treated.