If they are very strict try to find the right time like when they get home be patient, calm, polite and see to it they get rested a little bit and / or observe what mood your mom and dad first? Maybe better after dinner you can talk to them. If you are the eldest child just to make sure your younger sibling is away from the room while you are asking them for apporval, so that there are no interruptions while you are talking to them and of course they will consider the deciding factor such as your age, your health ( Like allergy concerns) reputable piercing shops ( registered place to go ), professinonal / certified piercer, how much or you can tell them that you can go with them at that piercing place together, if one of your parent is busy then, go with your mom or dad as long they approved it for you...
are you kidding? you don't need any permission to get piercings in your ears. I've got 6 piercings in my ears and I didn't want permission from my mum for any of them, I just called her and said "I've got 4 piercings in my ears, 5 piercings, 6 piercings..."
You're 16, that shouldn't be too much to ask. By the time I was 16 I'd already had around 15 piercings. Just bring it up and don't expect them to pay for it, it shouldn't be a big deal unless they're extremely strict.
That's an example pic by the way. :P