Let's start with some of the reasons why rationing existed. First, despite the United States being mostly self sufficient throughout the war, in some areas it wasn't. One oft-forgotten bit of the early part of the war was that it wasn't just military materiel like natural rubber that had become rare; palm and many other common frying oils of the time had been lost when the Japanese conquered large parts of Asia, and the U-Boat campaign reigned utter havoc on the main supply of sugar to the United States from Cuba.

More importantly, its allies weren't self-sufficient. I've written about this a few times before including here as different angles of the question on rationing keep coming up, and while most of this answer is adapted from that, you can read more there about some of the labor and political aspects I leave out for space requirements here.

Overall, though, the net effect of war requirements and exports created a strong recovery in the US economy in 1940-1941 as it became the arsenal of democracy, but the true boom times didn't happen until after Pearl Harbor. At that point, with full employment reached fairly shortly thereafter, money started chasing goods and services in all sectors, and inflation outright skyrocketed. Between December 1941 and March 1942, food prices alone went up 5 percent, and that was on top of the food and clothing index rising 20% over the full year preceding it.

The disruptions and potential for massive profits to be made speculating on what would be in short supply next led to something quite familiar to us nowadays. From V Was For Victory:

"A study of fourteen cities showed hoarding under way in many items: food (especially sugar, canned meats and vegetables, coffee, tea, spices, and olive oil), rubber goods (used automobile tires, gaskets for jars, garden hoses, golf balls, galoshes, girdles), household supplies (soap, linen, furniture, blankets), clothing (particularly men’s suits and shoes), and a miscellany of rifles and shotgun shells, typewriters, and paper clips."

This was not conducive to either price or labor stability for manufacturing, nor was it particularly helpful for the suddenly large purchases the United States military needed to make. At that point, FDR called in then-Justice and former Senator Jimmy Byrnes to become what he called "Assistant President", initially in charge of drafting war powers legislation (while still on the Court!) and creating the first of several agencies, the War Production Board, that began to control allocation of goods, and then later after he resigned from the bench first the Office of Economic Stabilization (which controlled all pricing and labor costs) and then even more powers as head of the Office of War Mobilization and Reconversion (the OWMR, which outright controlled all labor allocation on top of his other powers). In other words, Jimmy Byrnes was given control over the entire domestic portfolio with near dictatorial powers, with FDR only intervening occasionally as he concentrated on foreign policy and fighting the war.

The first thing that all the alphabet agencies accomplished was to implement rationing in April 1942 with War Ration Book #1, and unsurprisingly given the supply disruptions mentioned above the first things limited were sugar, butter and other fats, and red meat. All meats and other dairy rationing came in 1943, and while there was occasional grumbling about how much you could buy, the difference was that because of rationing everything indeed remained available on shelves provided that you indeed had coupons - and for once, most people could afford them. (One thing that reflects this is that meat consumption in the United States rose 1/3 between the start and end of the war despite rationing, a sign of just how thorough the recovery had spread through all economic stratas.)

This dovetailed with the massive effort made between government and the private sector to promote the efficacy and importance of rationing; this is where basic food groups developed for what was considered basic nutritional needs, where alternates were suggested for recipes, reuse of products considered, and where advertisements in magazines urged housewives to do their share with every last meal preparation. The social pressure to conform was immense, but it wasn't just that; as government issued coupons, it now became a crime to misuse them, something that even Justice William O. Douglas - later known for often obstinate protest against potential government overreach on civil liberties - authored a 1946 opinion in Davis v. United States upholding the conviction of someone who refused to turn over hundred of gasoline ration coupons for resale precisely because they were government issued.

The other aspect to this time period that's important to remember is just how much the economy boomed as well. Between 1938 and 1942 average family income had gone up anywhere between 15% to an almost unbelievable 150% depending on region, and one reason there wasn't more grumbling was because even if you couldn't spend it on rationed items you could spend it on other things. Country clubs, movie theaters, and racetracks boomed, housing prices went up 15-30% between 1941 and 1943 and then another 10-30% on top of that by 1944, and even despite all the spending household liquid assets went from $50 billion in 1941 to an astounding $140 billion by the end of 1944. In other words, a rising tide carried everyone, and it was one reason why there was very little protest on the home front.

But if you wanted to take a few risks, you could indeed get black market rationed items. Again from V Was For Victory:

"It was no problem to obtain scarce and rationed goods at a price in the black markets. Boneless ham in Washington, D.C. sold on the black market for $1.25 a pound, almost twice its legal ceiling price. With patience, a buyer could find nylon hose in most cities for five dollars a pair. In Philadelphia, without recourse to rationing coupons, a determined customer could buy five-dollar shoes for about seven dollars. Those “willful violations,” as an official of the Office of Price Administration said, were hard to prevent, since they occurred largely within regular retail channels on the basis of quiet collusion between the merchant and his patron."

So in other words, what price controls effectively did was to limit marginal demand on goods in short supply - except for those who really wanted to pay up for them surreptitiously. This too was one reason why there was little protest, since the societal pressure to conform to doing 'your part' was strong, but there was always a discreet supply available if you really needed something with relatively little risk of getting caught - just as long as you didn't flaunt it.

Probably the biggest example of this was in terms of gasoline rationing, where by the end of the war even contemporary reports suggested something like 15% of all gasoline production somehow didn't make it to official channels. The Davis case makes a bit more sense in that context; the appealable issue was about unlawful search and seizure of the rationing coupons - which were being crosschecked against the storage tanks to see how much gasoline the service station owner had sold - but the reason the whole thing came to light in the first place was the owner had been incredibly greedy. At a time in which gasoline was fixed at $0.21 per gallon, if you didn't have coupons the report was that he'd sell you as much as you wanted for the low, low price of $0.20 per gallon more (the price at which undercover agents pulling up to the station were able to purchase black market gasoline effortlessly.) Precisely who tipped off the agents making the raid has been lost to time, but I think it's fair to speculate that a disgruntled customer feeling like they got ripped off may have been the source.

A more somber incident where rationing played some role were the Zoot Suit riots, covered ably by /u/cdesmoulins here. I want to make it clear that I'm firmly in the camp that there's little doubt racism was the main driver of the incident; the segregated and overwhelmingly white Navy in its infinite wisdom planted their largest communications school smack dab in the midst of heavily Hispanic Chavez Ravine, just the location of which was massively problematic, and mainstream California political historians like Kevin Starr and Jim Newton have effectively traced the ugly and at times violent state of White-Hispanic race relations in Southern California to decades before that.

That being said, even Eduardo Obregón Pagán in writing a more social history, Murder at the Sleepy Lagoon: Zoot Suits, Race, and Riot in Wartime L.A., was genuinely surprised at how his research pointed towards the amount of civilians involved, whose anger often was shown by tearing up the Zoot Suits themselves. That makes the rationing angle hard to pass up; clothing material was distinctly restricted, and an overt display of suits that were not just new but oversized (and thus perceived as especially wasteful) in flagrant disregard of rationing restrictions clearly played some role in the conflict. How much? We'll never really know, but the rationing angle has been brought up by a number of other historians, and it's hard to argue that this wasn't at least a small part of the mindset of both why the Zoot Suiters chose to wear them as well as part of the internal justification for those who violently attacked them.