As in, did they load up on supplies and go out for days/weeks at a time and sleep in the tank or camp out? Did they generally return to a "base camp" every couple days. Was there a whole mobile support system that followed them? Mostly curious about US tanks being on foreign soil and trying I would assume to advance the front.
Here, I'll describe what the life of a tanker was like in the field, the various things they carried on their tanks, and who they would have to deal with in their battalion in order to draw their food and supplies and keep their tank in running order.
Food
While attacking (which during the race across France in August and September 1944 and the final drive into Germany, Austria, and Czechoslovakia in March, April, and May 1945 lasted for several days or even weeks due to the speed of the Allied advance, up to 60 miles a day!) tank crews were to subside on boxed C and K rations, when hot food such as sandwiches or coffee could not be brought up from the rear. The crews often substituted their Army-issue food (which could be harsh on the digestive tract) with local food. This food could include various items bummed or stolen from local civilian houses (inhabited or not) such as bread, meat, wine, or cheese, and even prepared meals abandoned on the table! Many tankers in their spare time obtained a rifle and hunted deer or rabbits, or got milk from cows if there was a farm boy in the crew. A humorous incident revolves around a battalion bivouac at night; a tank crewman heard a rustling in the bushes in the distance. When he called out, he got no response, so he fired his rifle at the bushes, later hearing distressed mooing. As you can imagine, there was dinner. They roasted the cow over an open fire and carved the beef. Some tanks even carried on the rear deck the carcass of a cow or deer for use later, although I question how sanitary this was!
Each tank battalion, had in its Headquarters and Headquarters Company a 16-man Administrative, Mess, and Supply Section. To perform its kitchen function, it had a 2 1/2 ton truck with a 1 ton cargo trailer. The truck had a bazooka for self-defense. The section handled various administrative and personnel functions, such as distributing mail, and coordinated the battalion's feeding. They also served as rear area security when necessary.
Handling and distribution of replacements was left up to the battalion's Administrative and Personnel Section in the Service Company.
Personnel:
1 First Sergeant (section commander)
2 Staff Sergeants (mess and supply sergeants)
1 Corporal (company clerk)
2 Technician 4th Grade (cook)
2 Technician 5th Grade (cook)
1 Pvt./Pfc. (cook's helper)
1 Technician 5th Grade or Pvt./Pfc. (driver)
6 Pvt./Pfc. (basic)
Vehicles/Equipment:
Each light and medium tank company, as well as the as the Service Company of each tank battalion also had its own, smaller (13 men), Administrative, Mess, and Supply section that cooperated with the battalion and furnished food items not as urgent. If the whole battalion sat down for a rest, the higher-echelon section took over, preparing most of the food and giving it to the company sections for distribution to the tankers. Otherwise, the companies' respective sections handled most of their food and minor personnel needs when resting or moving slowly enough.
Each tank or Service Company's section also had a 2 1/2 ton truck with 1-ton cargo trailer, except this time the truck had a mounted .50 caliber machine gun instead of a bazooka.
Personnel:
1 First Sergeant (section commander)
2 Staff Sergeant (mess and supply sergeants)
1 Corporal (company clerk)
1 Technician 4th Grade (cook)
1 Technician 5th Grade (cook)
1 Pvt./Pfc. (cook's helper)
1 Technician 5th Grade or Pvt./Pfc. (driver)
5 Pvt./Pfc. (basic)
Vehicles/Equipment:
The Things They Carried
Many items you would expect to find on tanks or tank destroyers, besides the issued shovel, sledgehammer, axe, mattock, crowbar, tensioning wrench, and engine crank (radial-engined Shermans and M18 Hellcats only) included:
Boxes of C and K rations
Boxes, crates, or casks of wine, beer, and local food
"Liberated" enemy equipment like rifles, helmets, and other trophies
The crew's equipment that was too bulky to keep inside the tank, such as blankets, tarps, musette bags, sleeping bags, ammunition bags, helmets, various changes of clothes, etc
Camouflage net and a length of chain or rope
A spare road wheel, length of track, or extra volute spring or other equipment. Spare tracks were often used as supplemental armor
Extra tools wrapped up in a blanket or tarp (infantry liked to steal these as they were full-sized, compared to their entrenching tools)
Machine gun ammunition in their respective ammo cans. Several thousand more rounds than the allotted 4,000-6,000 were often carried
More packaged .30 and .50 caliber machine gun and carbine/Grease gun ammunition still in their sealed wooden crates
A tripod for the .50 or .30 caliber machine guns
Cans of gasoline or water, and a can or two of oil, and buckets to carry it. Fresh water was often hard to come by, and nobody wants to run out of gas when you're chasing the enemy.
Assorted stuff, including but not limited to bicycles. Stoves with lengths of flue pipe were also carried, in order to cook food. Logs were often lashed to the sides or front of the tank, to be placed under the tracks in order to give traction to escape from the mud or to surmount a hill. A quest of mine is to find the weirdest item a tank crew carried in their stowage.
Oftentimes, this was draped over with a tarp and tied down with a rope through the lifting rings, topped with the week's color of air recognition panel (red, yellow, white, or a combination of two) Crews often fashioned better ways to carry equipment on the rear deck or back of the turret, making frames with sheet metal or pieces of wood to stop their possessions from falling off the tank. Later Shermans had a foldable rack for the crew's possessions on the rear of the tank, but this was still not enough. Many tanks (especially ones armed with the 105 mm howitzer) were issued with a 1-ton ammunition trailer per the TO&E; crews often carried their things in there in lieu of ammunition.
Tank destroyer crews faced the same problem as tank crews. They had nearly no space inside their vehicles to store equipment and gear, and they soon took on just as much of a "pack-rat" appearance as the tanks! The level of stowage carried on tanks and tank destroyers tended to intensify as warfare became more mobile and crews spent more time away from their bivouac.
Sleeping
When US tank or tank destroyer crews got ready to bed down for the night, they sometimes took a large tarp or blanket and draped it over the side of the tank, in order to have something to sleep under. If they were under risk of enemy fire, they dug a shallow pit the width of the tank, and drove the tank over it; this way, they could sleep and be protected from shrapnel if artillery hit nearby. Sleeping inside the tank would seem like a very uncomfortable proposition. I'll use this model kit of a Sherman with a full interior as an example. It's very cramped inside and there aren't very many spaces, if anywhere at all, to lie down flat.
Maintenance and Fueling
If the tank broke down, the crew usually tried to perform minor maintenance on it. If it was seriously busted (blown head gasket or broken propeller shaft; the Sherman was a reliable tank, but it was not completely free of mechanical problems), it was towed away, to be fixed by the battalion's maintenance platoon (located in the service company) For this task, the platoon had two M32 tank recovery vehicles, and two M1A1 wrecker trucks, plus tools and various personnel like mechanics and welders. Each tank company headquarters also had an M32 for their own use.
Personnel:
1 Captain (motor transport)
1 Warrant Officer (motor transport)
1 Master Sergeant (motor)
1 Technical Sergeant (recovery chief)
1 Staff Sergeant (mechanic chief)
1 Sergeant (motor supply)
28 Technicians 4th and 5th Grade (welders, artillery, tank, radio, and automotive mechanics)
Vehicles/Equipment:
2 M32 tank recovery vehicles
2 M1A1 wrecker trucks
2 2 1/2 ton cargo trucks with 1 ton cargo trailers
1 3/4 ton truck
1 1/4 ton truck
The battalion's supply and transport platoon (also in the service company) of 29 2 1/2 ton trucks moved around the ammunition, fuel, oil, and lubricants for the tank battalion. The TO&E does not specify beyond "Truck, 2 1/2 ton, 6x6, cargo" but there probably were tanker trucks for the fuel and water.
Personnel:
1 Lieutenant (platoon leader)
1 Warrant Officer (supply)
1 Technical Sergeant (supply)
2 Staff Sergeants (platoon and supply sergeants)
3 Corporals (dispatcher and 2 clerks)
29 Technician 5th Grade or Pvt./Pfc. (truck drivers)
7 Pvt./Pfc. (ammunition handler)
7 Pvt./Pfc. (machine gunner)
Vehicles/Equipment:
29 2 1/2 ton cargo trucks with either 1 ton cargo or ammunition trailers for fuel and lubricants (14), ammunition, (13) water, (1) and rations (1)
1 3/4 ton truck
1 1/4 ton truck
14 trucks were to be mounted with machine guns and 7 of them were to have bazookas.
Sources:
Steel Victory: The Heroic Story of America's Independent Tank Battalions at War in Europe, by Harry Yeide
The Guns at Last Light: The War in Western Europe 1944-1945, by Rick Atkinson
Armored Thunderbolt: The US Army Sherman in World War II, by Steven J. Zaloga
Judging by FM 17-33's (1944) section on bivouacs, the system hasn't changed much from then to today.
Generally speaking, you would live on your tank. Your tank carries an amount of your personal gear, the majority of it is hauled around by the First Sergeant's truck. (Today's tanks have more storage space on the tank).
When the battalion had gotten to wherever it was going, it would set up a laager/bivouac area, with the line units forming the perimeter, and the command/headquarters/service (Maintenance) elements in the middle. Fuel, food and supplies would be brought to the central area, and, in the words of the manual, "Fuel and ammunition vehicles may be brought up to each tank or may be halted in a central spot under cover and the supplies carried to the individual tanks by their crews, whichever can be done more conveniently and safely."
It would be possible for a unit to be brought out of the line for a while for R&R, in which case they would have access to higher levels of support, to include field shower units, better chow halls, etc.