How do I get a fitted sheet that will fit my Queen size mattress well?

Here's a tutorial on how to fold a fitted sheet: https://www.realsimple.com/home-organizing/cleaning/laundry/fold-fitted-sheet

And here's something I saw the other day on how to use bungee cords to get a truly TIGHT fitted sheet around a mattress. https://imgur.com/ofEhcit

Most fitted sheets are made to fit up to 18" mattresses. You can look for sheets that have a lower height accomodation for a tighter fit. You might take in the sheets you currently have.

As for folding, I always match up the corner lengthwise then again and tuck inside each other. Then lay flat and fold down the 2 sides that have elastic until I have a rectangle that isn't gathered. I fold my flat sheet to the same size and lay on top of the fitted sheet. Then add the pillowcases and fold to a smaller rectangle. A lot of people save out one pillow case and place sheets and pillowcases inside the 1 case. Then fold over. I rarely do this but it's a neat way to keep everything together.

Amazon sells sheets for shallow depth (6-9") mattresses. If you google this, I'm sure you'll locate other retailers.