Distillers Grains are a byproduct of the distillation process. There are two main sources of these grains. The traditional sources were from brewers (beer) an more recently, ethanol plants are a growing source. It is created in distilleries by drying the mash.
How much to feed depends on who or what you are feeding. We give all our cows that calve DDG's for about two weeks after calving, around 10 pounds wet (it has a small particle size, so blows away easily. We add water to it when we feed it, make it like a mash, and the cows are less likely to spill it and eat it like candy). I feel like our cows come into their milk better when we do this. Might be crazy, but we do not calve a bunch of cows so for us it works. Especially for our first time calvers, and that way they come up so we can check them and the calf visually to make sure all looks OK. If we are showing a pair, the cow will stay on the DDG to help keep her weight up. It is cheaper and fattens better than a show grain.
Just what we do. And it works. Although recently the price has really gone up (but the price of ALL grain has gone up!). Here is one of our show cows enjoying her DDG's