It's pretty simple. For the 1947 501, size up by one inch, going by measured size rather than tag size (because a pair of 1947 tagged 32 might come out a different size, depending on when it was produced). So if you're buying online, get your seller to measure the jeans by putting them flat, stretching them a little so that both front and back line up. For the 1947, that measurement, raw and unwashed, needs to be one inch bigger than the actual measurement of jeans that fit you well around the waist.
Levi's recommend you to size up by one 'size', ie two inches. But one inch is better for most models, as it allows for the jeans shrinking two inches in the wash - but it also accounts for one inch of stretch.
That's it. Some people obsess about how you shrink your 47 before you wear them - but most methods end up the same, after a wash or two. For mild shrinking, cold soak briefly; for maximum shrinking, put them through the washer, inside out, no soap, at 95 celsius. (Don't put them in the dryer, it will leach out resins and take some indigo with it). Don't add salt; don't add vinegar. Save those for your fish and chips, they have no effect on denim.
For 1955 501, the issue is pretty different. The '55 is a distinctly different cut; it has more of a shoulder beneath the waistband, more generous thighs, and most crucially, it's bigger across the seat. Hence for the 1955, you should buy your actual waist size; then once you've soaked the jeans either put a piece of wood in the waistband as it dries, wear the jeans as they dry, or be prepared for a tight waist for the first couple of days of wear. Doing so will give you a classic, vintage fit. Buying actual size in the 1947 won't normally work because the thighs and seat will be too tight.
The difference between the sizing for both pairs shows some of the subtleties of jeans design. The 47 and 55 are classic cuts (some people reckon LVC's take on the 1947 exaggerates the slimness of the 47, but no matter) which serve as a model, or shorthand, for countless pairs. Hence I know my Studio D'Artisan 103XX are a 47 cut - slimmer thighs, a straight line down from the waistband, whereas other models, like some classic Sugar Cane, have that higher rise, and that distinctive shoulder associated with the 55.
My main pairs came 34 raw (for the 1947) and 32 raw (for the 55). Compare them side by side and you'll see how, despite being nominally smaller, the 1955, on the right, is actually bulkier despite having a waist that started out slightly smaller.
What this photo doesn't really show is the difference in denim between the two pairs - both on the LVC reproductions, with denim made by Cone, and on the original. For fabric nerds, the two manifestations of the denim are as distinct as the shape.
|1947 501, tagged 34, on the left, 1955 501 tagged 32 on the right. The waists have shrunk/stretched to similar sizes, but the 1955 jeans, as you can see, are still more generous around the seat.|
What about other Levi's? That's a story for another day; eventually I'll transfer all the info I've written on the evolution of the 501 design, and fitting, to this site. For the time being, bear in mind that LVC models from 1901 and earlier use Japanese denim, made by Kurabo, rather than the American Cone denim, used for the models from 1915 on. The Japanese denim shrinks less. Ah well, time to check my SuperFuture inbox.