Tanks are generally recovered using Armored Recovery Vehicles ARV sometimes called a Tank Recovery Vehicle TRV. Now the recipe for building a good ARV/TRV is very simple. First find an existing tank. Then take off the gun. Then put on a big winch. Customize - add A frame cranes or additional winches or weld on eyes for chaining together multiple vehicles for pulling the broken Tank.

The US in WW2 had the M31 TRV based on the M3 Grant chassis and the M32 TRV based on the M4 Sherman chassis. As far as I can tell the US was the only country in WW2 to factory build Tank Recovery Vehicles. Other forces seem to have modified existing tanks in the field. The Soviet Union and Britain extensively used M31 and M32 TRV.

The easiest way to recover a broken down tank was to fix it and drive it. All forces had mechanic trucks with spare parts, heavy duty jacks, extra fuel, welding equipment etc.

ARV/TRV weren't always available. If a tank was broken down in the middle of a road soldiers would have to find ways to move it. I read one account from Italy where British soldiers place a steel sheet under a broken German tank and used explosives to roll the tank out of the way. I read another account from France where US troops attached several winches to a tank and used a tree as an anchor to roll the tank out of the way (I'm going to try to find the text of this account because it gives a really good idea of how difficult it was to move 40 tons of steel). A final account I read used several trucks chained together to pull a tank out of the road.

Of course the hardest part of recovering a broken down tank was cleaning out the previous crew. This duty was voluntary and was normally taken on by the chaplains with other volunteers.

For the Germans Tiger tanks were often too heavy to be recovered. Special TRV's were made to handle the heavier tank but because these weren't always available many of these tanks were simply abandoned after they broke down.

Our current (US) maintenance doctrine was initially developed from lessons learned in WW2. Each Tank BN had it's own maintenance team that had mechanics, recovery vehicles, some spare parts, basic welding and cutting tools. These guys could do basic repair in the field. Right behind them would be a maint element attached to a Bde or Regimental level command. Same basic setup but with improved capabilities. Usually this level could repair almost anything on a tank except significant hull damage. Depots were much farther behind and could basically rebuild a tank from the ground up. I was an Infantry Battalion Maint Officer in the 70's so had a lot of interest in this subject.