Every year in fall I don't know whether I should dig up the soil, add compost, or if I can just get by with mulching. Maybe there's some tried-and-true method so the soil is fertile come spring?
Digging is fine, but it's not a must; the main thing is to add organic matter. I usually spread compost or well-rotted manure in the fall in a layer about 5-10 centimeters thick right on the bed, and on top of that - leaves or grass for mulch. Over the winter all of it will break down, the soil will become loose and nutrient-rich, and in spring you can plant right away.
If the bed is completely depleted or diseased plants were growing there, then yeah, it's better to dig it over deeper and mulch it well. But if the soil is fine, you just add compost with mulch on top - and you're done, come spring it'll be amazing. The key is having enough organic matter; I usually go generous with it, no stinting. My neighbor recommended sowing cover crops in the fall too (peas, rye) - they're cheap and really boost the soil, but that's only if you want to go the extra mile.
Try a combined approach: in September, spread organic matter right on top of the soil (compost, manure, leaves), and don't rush to dig it in until spring. Over the fall and winter, soil organisms will do half the work, everything will mix naturally, and in spring you'll just need to level it out and do a light dig before planting. It saves you effort and gives better results than fall tilling - the soil gets time to recover and becomes loose on its own.
Soil that yields crops year after year naturally becomes depleted - plants pull out nutrients, and rainfall leaches away minerals. You definitely need to restore fertility, but the approach depends on what condition your soil is in right now.
If the bed is compacted and water pools on it after rain, you'll need to dig it over - at least shallow digging, 15 - 20 centimeters deep, to break up that dense layer. If the soil is loose and drains well, you can skip the spade. Either way, I then spread compost or well-rotted manure in a 5 - 7 centimeter layer right on top, and then mulch with leaves or grass about 10 centimeters thick. Over winter and spring, the organic matter and mulch will settle down, soil organisms will break it all down, and by planting time your soil will be soft and nutrient-rich.
Lifehack: in fall, lay cardboard or newspaper in several layers on the bed, then dump compost and mulch on top. By spring the cardboard will decompose, become part of the soil, and improve its structure. Works especially well on beds that used to have weeds or a hard crust.
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