Making good hay depends on a lot of things. Primarily the weather and the quality of the pasture from which it's cut. We only get one cutting a year here except for alfalfa. So, alfalfa hay is a little different story and alfalfa fields can vary a lot in quality.
Hay will usually consist of a primary grass(whatever had been sown in that field or a mixture of grasses.
Some hay fields can have a lot of brush or briars growing up in them in which case there's sticks and thorny strands that have no food value for horses and cows.
Whoever you buy from should be able to tell you what kind of grass it is. We had fields of orchard grass, brome grass, ladino and fescue.
Timing the cutting is critical but mother nature has a lot to do with it. You want the grass mature but not overly so. That way you get the good volume and grass is going to seed but is still green to keep good nutrition content.
If it's been very dry, the hay will be dusty, there's no way around that. If it's been dry a long time the grass will be poor quality or you just won't be able to make hay. You need dry weather for several days so the hay can cure after cutting before baling.
If it isn't dry enough before raking and baling it will mold. If it gets a shower on it, it will probably mold. If it gets rained on after baling before being properly covering or put up, it will mold.
Haying time is a busy - dawn to dusk, hot, dusty, scratchy chore and the amount and quality of the winter's feed depends on a few days task.
When the baler picks up the hay from the windrow a press continually smashes bunches into a square chute which makes the flakes(sections of the bale). You can reach in between them and pull some out and look for mold. You also want to look for sticks protruding from the bale. If you don't see any, the field was probably pretty clean. The grass should be dry but still have a fairly green tint to it(unlike straw). Some parts of the country have huge fields of high quality grass but we were mostly forested with most fields of only 5 to 20 acres and the forest was constantly trying to take them back.