Living with parents presents it's own challenges. There's
this guide on hiding diapers in the articles subsection of the forums.
It covers the bases pretty well. I will offer some anecdotal advice. The best place to hide something is in plain sight.
Step one:
Tell your parents that you would like some totes to organize your personal things, room, clothes, hobby, project, whatever. Then buy one or two 20 gallon plastic totes with lids, should cost about 7$ apiece at like a Walmart or Target. Not the clear one's obviously! The great thing about this is that you're not lying. You do need them to organize some things, you're just omitting specifically what those things are. And they won't be likely to go scrummaging inside them because you created a mental precedent that they are for storing stuff other than diapers.
Step two:
Actually getting the diapers. You can do an actual pharmacy, or medical supply place. Don't worry about being judged about buying adult diapers. Just go in and buy them like you've been there a million times, and you own the place an nobody will think anything of it. A normal pack of diapers like Depends, Attends, CVC brand whatever will fit inside a standard backpack. Come home, walk in like you always do, take your backpack to your room and put them inside the previously acquired tote. Take the diapers out of the packaging, and place them in the bottom, and then fill the tote the rest of the way with other things you are "storing". Put it in your closet. Put the packaging bag from the diapers back in your backpack and dispose of it at some other location other than your house.
Ordering off the internet.
This is trickier. You need some means of ordering online, credit, debit card, or paypal. Then you need to get the money on it. Then you need to have a place to have it sent. If you know exactly what time the postman comes you can have them sent by standard post and plan ahead to intercept the delivery. Fedex, UPS, and other parcel handlers can be unpredictable. If it's coming straight to your house and you don't want the 'rents to find the box, you must be 100% on being able to get to the house before they do, or be there when it is delivered.
The best plan would be to a non-family friend, who knows you are ABDL and is supportive, receive the parcel and hold for you until you can pick them up.
Step three:
You got the diapers, and now you've worn and used one. Disposal of a wet/messy diaper is tricky expecially living with parents. This is always going to be a gamble in getting caught. I used to live with roommates and I needed to keep my diapering somewhat discreet. So I would use old plastic grocery bags to put my used diapers in, tie off the tops tight, put them in a larger garbage bag, store that in a separate airtight tote, and then I would throw them out the night before the trash man came so they weren't sitting around in the rubbish bin to be discovered.
My personal caveat.
Honesty is best policy. There's all kinds of potential negatives to coming out to your parents, but you also need to deal with the reality that if you do this for long enough, you will face the very real possibility of getting found out. And that can blow up worse than if you had simply been honest with them in the first place.
I know I become disappointed in my children when I find that they have been devious and sneaking things behind my back. So this is a tough decision to make for you.
Is it better that they find out before you go doing a whole lot of sneaking behind their back? Possibly, but that's something you need to gauge with your parents. Are they likely to be supportive of you? Are they hyper-conservative? Are they socially liberal?