Once nobody was willing or able to use them(either in other conflicts or as bulldozers), tanks were stripped of any particularly valuable or reusable parts, and whatever was left was disassembled/cut up to be used as scrap metal.
(All of the images and detail can be found here or here.)
Vehicles which were destroyed on the battlefield were recovered to either be repaired or stripped. The recovery operations were aided by specialized vehicles(such as the M32) which could move the disabled tanks to scrapyards:
At the scrapyards(also called "strip out yards"), the valuable bits that still worked were removed from the disabled tanks to be used as replacements in more usable tanks. This was also a great time for military research, as engineers could poke around allied and enemy tanks looking for vulnerabilities and areas of improvement.
As for the rest, whatever could be removed from the hull or cut up using on-site tools was piled together. If there were no on-site tools to cut up the tank hulls, then the hulls were shipped to better equipped processing facilities elsewhere. Once disassembled, whatever couldn't be directly used for other tanks was used as regular scrap metal wherever metal was needed:
However, once the war was over there were still hundreds of thousands of working vehicles that needed a home. For those that didn't get sold/lent to other countries for other conflicts, there was plenty of room in military depots like those in the American Southwest:
In the years after WWII, the vehicles that weren't expected to ever be used again were stripped, chopped up, and scraped in pretty much the same way as those in the post-battlefield scrapyards(though with much less urgency):
A few of those that weren't scrapped were converted to monuments(as you found) or stored/refurbished in museums or private collections, but many chose a much more humble retirement and were cheaply sold to farmers to be used as tractors(ammo not included):