Are people supposed to thank the flag for its service before binning it?

Return flag(s) to participating retail stores who will dispose of them.

Flags made of natural fibers (wool, cotton, linen) should be burned in a dignified manner; privately without ceremony or public attention being drawn to the destruction of the material.

Flags made of synthetic material (nylon or polyester) should be respectfully torn into strips, with each element of the flag reduced to a single colour, so that the remaining pieces do not resemble a flag. The individual pieces should then be placed in a bag for disposal – the shreds of fabric should not be re-used or fashioned into anything.

Based on my quick google. I'm guessing they're handling burning them / shredding them.

My parents told me they go to a farm far away.

When I was a kid, I was told that you were supposed to burn a flag if it touched the ground so, being a kid and fascinated by fire, I would go to great lengths to make sure flags found their way onto the ground so I could burn them. I would have been immensely disappointed if this had been a thing instead.