As I eagerly await the first beets of spring, I just finished last year's. In November I went to Vermont, where my father-in-law lives, and where I have a farmer friend. I asked her for every long-keeping thing she could spare that would fit in my refrigerator, and she gave me an assortment of winter squash and potatoes, Brussels sprouts and a cabbage, carrots and turnips, garlic and onions, and beets. Some of the beets sat there until last week, when I noticed one of them beginning to get some odd white spots: not bad, three months in the fridge. (I still have a few carrots, and two potatoes; they're fine.)
This is how it used to be in the north, of course, before you could get eggplant in January: the gap between fall and spring was filled with roots (carrots, beets, turnips) tubers (potatoes), and winter squashes. And the roots are perhaps the most valuable of these, because not only do they overwinter well but they're among the first vegetables we see in the spring.
Beets are number one on almost no one's list, but their combination of sweetness and earthiness is literally unique, and the fact that you can eat their greens - which are almost identical to Swiss chard, Swiss chard being essentially a beet that is grown for its greens rather than its root - makes them doubly useful. They are, however, mistreated, and widely despised for their renown staining abilities.
If you boil beets, then peel them, you leave about half of their flavor behind, and you're stuck with a soggy vegetable that ruins your clothes, unless you're thoughtful enough to wear an apron (I'm not), in which case you ruin that. If you bake them, however, the result is drier, more flavorful, less messy. If you eat them raw - well, the staining dangers actually multiply, but the flavor is insanely good, and they're delightfully crunchy. And if you turn them into pasta sauce, as I did the other day, you create a surprising, very red, and rather delicious dinner.
To take these one at a time: I first learned how to bake beets about 15 years ago, and it immediately became my go-to basic recipe. Essentially, you wash them, wrap them individually in foil, and throw them in the oven. (Think restaurant-style baked potatoes, but better.) When they're ready, the skins slip right off; really. This method has the advantages mentioned above, plus one other: you can keep them in the refrigerator, wrapped and cooked, until you're ready to eat them, for at least a couple of days. (If you know you're eating them right away, you can skip the foil and bake them in a covered dish with a tiny bit of water.) When you want to eat them, unwrap and peel, then slice and heat in butter or oil, eat them cold, or use them in any other cooked beet recipe.
Few people even know you can eat beets raw, but there's nothing weird about it. (You can eat turnips raw, too, but that's another story.) Peel them, with a peeler; they're not as messy as they are after being boiled, but you'll still want to do this over the sink. Grate them; I use a food processor, because I want to minimize the mess, but if you're a luddite or a masochist you can grate them by hand. Toss them with a vinaigrette, preferably one with olive oil, sherry vinegar, shallots, and mustard. A better salad you'll never eat, nor a more beautiful one: ordinary beets are truly garnet-colored when raw, and the oil makes them glisten.
Finally: When I noticed, the other day, that I had to cook the last of last fall's beets or lose them, I peeled them and grated them, but since it felt like a pasta night, and since I had some vague memory of making beet-stuffed ravioli once, I decided to turn them into a sauce. I put them in a pan with a little garlic, thyme, chopped onion, and oil, and cooked them with alternating splashes of white wine and water, until they were pretty soft. Meanwhile, I cooked pasta. When I tossed them together, the pasta immediately turned red, not tomato-sauce red, but bright red; this isn't the most common color in the pasta world, but it's not unappealing. Because of the beets' sweetness, I added a large mound of grated Parmesan, which did the trick: sweet, earthy, salty, sharp - pasta doesn't get much better than that, and now I can wait another month or so for the first beets of spring.