The food supply system consisted primarily of a company or battalion field kitchen section that prepared and cooked hot rations daily, which were then delivered to the front by various means such as by horse, foot or truck.

In the early war Blitzkreig, it was difficult delivering rations to the front until positions were stabilised, having to transport supplies across muddy trails and damaged roads, in some cases even under fire. Keeping up with the fast moving front line was not an easy task. Later in the war it was pretty much the same problem, difficulty getting the supplies to the troops. Throughout the course of WWII, the Germans never modernised their food supply system.

By the later years of the war, the supply system was failing to keep the German army fed, troops would be found going without food for extended periods of time, no doubt a great morale killer and also couldn't have been healthy at all - especially when in a combat environment.

Accounts from the Battle of the Bulge, 1944:

Grenadiers Ulrich Jonath and Horst Hennig, 2nd Battalion, GR 914, 352nd VGD, summarized the overall situation of the German Army‘s attempts to feed its men during the Battle of the Bulge, including how they were able to survive the campaign, “Our food supplies were unsatisfactory. Other than captured American chocolate and some preserves taken from civilian houses, there was nothing."

Unteroffizer Wilhelm Stetter, 3rd Company, 1st BN, GR915, also stated the following about receiving a much-need issue of soup, “We had our first warm food in ten days, pea soup on which the fat was swimming, for there was plenty of pork fat in the deserted houses. So we ate, no, we gobbled as much of the fatty broth as we could hold; serious digestive disturbances and stomach cramps were to follow two days later.”

Hebert Brach, 6th company, 2nd BN, GR916, had this to say after finally receiving his first German rations in days, “When we had reached the foot of the hill, there stood a soldier with a loaf of bread in his hand, cutting off slice after slice, which our men practically tore out of his hand, for we had waited six days for rations, since the supply train could not be brought closer because of enemy fire. And this slice of bread was welcome to us; we were practically starving, and this bread tasted wonderful.”

Troops became more and more reliant on combat rations with field kitchens struggling to get the hot meals through to them. Often the troops would be short on rations until supplies arrived, during that time they would have to survive on combat rations (known as 'iron rations') or food obtained from locals in the area - plundering, however, was punished by the high command. Combat ration menus and quantity varied very little so troops often relied on local food.

The quality of food also dropped but not dramatically, by all means it was still suitable and while not up to the best standards, would've tasted great to a hungry Landser. Even post war US tests on the rations found them to be acceptable, some almost quite tasty, however they thought some items of food tasted strange or unsatisfactory.

As for the food itself:

Once the rations arrived at the front in thermos flasks, the soldiers would then go and pick them up as they were handed out in individual containers, they then usually put the rations into mess tins, canteens, pots or bread bags.

The bread bag could carry cutlery in one of its two compartments and the canteen came with a metal (or Bakelite) cup which could be used to heat tea or coffee over a fire. The mess tin (called a 'Kochgeschirr' or 'cooking pot') had a lid that could be used as a frying pan. All very practical for food uses. Small Esbit cookers were used by soldiers and had smokeless tablets which allowed them to cook even in combat conditions. It was like a small portable kitchen.

Breakfast included bread - generally baked the day before - marmalade, a solid honey substitute and some canned food, coffee, chicory or malt and margarine. Sometimes animal fat and butter was available.

Lunch was the hot dish of the day, pots and thermos flasks filled with stew - usually composed of potatoes, fat, legumes of some sort and anything of animal origin that added taste and colour. In cases of supply difficulties, canned soups were distributed instead.

Dinner was a cold meal that usually consisted of canned meat or fish, margarine and a drink of a hot beverage to keep soldiers alert during long nights.

Although the menu was rather monotonous, food could arrive in parcels from home and extras could be purchased at the canteen such as canned food, seasonings and candy.

The full combat ration was made up of 300 grams of hard crackers, 200 grams of preserved meat, 150 grams of preserved or dehydrated vegetables or pea sausage, 25 grams of artificial substitute coffee and 25 grams of salt. The smaller half portion consisted of the canned meat and crackers only. These 'iron rations' were to be consumed ONLY when it was not possible to obtain food from a field kitchen.

I read some letters my grandfather wrote to his father. It's only a snapshot and not a timeline like you asked, but perhaps it can give you an insight. I hope this counts as source and not as anecdote.

He joined the Waffen-SS in late 1943 or early 44, directly after school, eager to "fight for his country". He had a teacher who had persuaded the whole class to volunteer together. He was then stationed in the Netherlands. The western front didn't even exist.
He wrote home that they often didn't have anything to eat. And if they had food the quality wasn't very good. Later, stationed in the Normandy as scout, he would eat what the residents left there.

I find that very interesting, because the SS is always portrayed as the elite force with superior equipment.