Blemish treatments varied with the era, and I imagine also with an individual's social class and aspirations. Renaissance-era beauty recipes take clear unblemished skin as an implicit goal for women, as well as fair skin in the sense of paleness. One image of skincare in this era might be the idea of makeup as a cover-up -- writers describing Elizabethan makeup often go down a bit of a fanciful route regarding slathering on white lead to cover raging pustules and smallpox scars, and no doubt people did this, but there was an interest in prevention of skin blemishes as well as hiding the unavoidable marks left behind.There are abundant late medieval and Early Modern sources describing recipes for home skincare treatments, right alongside recipes for makeup and hair treatments as well as medical advice for more serious issues like toothache or gout. These recipes were compiled in "books of secrets", and the advent of printing helped these books and their contents disseminate widely. All of these remedies would be prepared at home. Some recipes refer to removing "marks" or "blemishes" from the face -- this is a broad enough category to encompass other skin conditions besides acne vulgaris, but in some cases their composition and use are relatively familiar.
To remove marks from the face: Take iris roots and boil them in water until it is reduced by half, then purify and with this water wash the face and you will be free of blemishes
Or:
Water to make you beautiful: Take strong vinegar and lemons cut in pieces and put in a glass alembic and put in powdered cloves and whole cloves, a little of each, and put everything in the alembic and save the water which is perfect and use.
Both of these sound a little like modern toners -- vinegar and lemon juice are both astringents, though it's hard for me to puzzle out what iris root (modern orris-root, still used in skincare but more often in perfuming) is meant to alter on a practical level in order to eliminate blemishes, rather than as a cover-up. Because of the nature of these books and their cures, these recipes might have been in the hands of women and girls, but it's possible their use was extended to boys and men as well. Cosmetics might be off the table for 15th and 16th century men, but you could always grow a nice beard to cover it up -- though given the way beards sometimes interact with sensitive skin, that could backfire. In addition to all this, daily face-washing and steam baths were both common in Europe (contrary to pop culture images of absolutely filthy everybody) though use of steam baths in Italy tapered off later into the Renaissance. (They thought they were a little bit too German.)
Another Elizabethan skin-care option "against spots" given by Christopher Wirzung in his 1654 General practise of Physicke:
the Whites of two eggs mixed well with rose-water, plantain juice, and dock juice. Followed by the application of the following: 8 ounces of vinegar and rose-water, one ounce of brimstone [sulfur], one quarter of an ounce of alum--boiled softly until one-third has evaporated.
Again, a mix of both ingredients recognizable from modern skincare remedies (like rosewater) and ingredients that aren't, at least not in those terms. Alum is an astringent, and sulfur was also in use as a topical treatment for other dermatological issues like eczema -- sulfur affects some acne by diminishing sebum production. I can't say how well overall these remedies worked, and noting their ties to modern hippie-dippy acne remedies is by no means a suggestion to run out and stock up on dock juice, but these remedies aren't all necessarily fanciful.
Acne vulgaris in medieval and Early Modern texts is often linked or conflated with rosacea, and rosacea was linked to other conditions observed in connection with facial redness -- bashfulness and heavy drinking. In terms of shifting understandings of acne as a distinct phenomenon and its origins, Aristotle and Hippocrates' account of acne vulgaris linked it with puberty and beard growth; later Early Modern writers linked it to humoral imbalance, menstrual functions, or "venery" in young persons:
[Johnston's words in 1648], translated by Culpepper, state “vari are little hard tumours on the skin of the face curdled up of a hard thick juice. They are known easily. They are of the bigness of hemp seed, and they infect young people that are inclined to venery and fruitful, but chast withal and continent”.
Another author (Joseph Jakob Plenck) more succinctly says: Matrimonium varos curat. Marriage cures acne. But is it the sexual and emotional stability that comes with marriage that cures acne, or simply the passage of time as the youth matures to a marriageable age?
Being spotty wasn't desirable as such, nor was it seen as an endemic condition of all young people, but it's firmly grounded in the realm of the natural and the relatively treatable relative to other humoral conditions or evidences of internal dysfunction. Out of the multitude of other skin conditions known and described in contemporary texts of the 17th and 18th centuries, acne vulgaris without complications or unusual severity was small potatoes. Obviously not all cases of acne are so simple and uncomplicated, but a 19-year-old of either sex with a couple pimples wasn't in danger of being chased out of the community as a leper.
With advances in understanding of the skin and pores, scientists connected surface acne to follicular inflammation and sebaceous blockage -- 19th century writers now began to identify acne primarily with young men but also with young women:
English dermatologist Samuel Plumbe published A practical treatise on the diseases of the skin in 183. He described blockage of the sebaceous glands as follows: “it has been constantly observed, that persons of sanguine temperament and florid complexion have been most subject to follicular inflammation; and among these, that young men between the ages of 20 and 25 have been the greatest sufferers from it. Females, at the same age, are also subjects in whom its visitations are not infrequently manifested, but, in the latter, it rarely proceeds with such rapidity to suppuration, or produces such unpleasant appearances as to extent".
Subsequent treatments for acne in the 18th and 19th century remained mostly topical but shifted toward store-bought and pharmaceutical solutions -- both innocuous herbal remedies and medical treatments containing toxins like arsenic. Acne as a medical condition was a condition of young people, but only a matter of pressing concern to middle- and upper-class young women. Skin conditions we'd today recognize as at least potentially "adult acne" might have been swept under another skincare category, or treated with the same topical remedies of questionable efficacy as for other skin concerns like discolorations.
Some sources:
Tessa Storey's Book Of Secrets Database allowing to search these texts by ingredients, ailments they were intended to treat, and more
N.F. Mahmood, A.R. Shipman, "The age-old problem of acne" (2016)
There are also a couple interesting past threads about acne (on top of /u/Mictlantecuhtli's fascinating discovery) including more recs for books of secrets!
Was acne so widespread in the past as it is today? answered by /u/notheretoargue, /u/dmrose, and /u/Little_Noodles
How come we never see historical people depicted with acne? answered by /u/Bethamphetamine
Was acne more or less common in ancient civilizations, or even a few hundred years ago? answered from a scientific angle by /u/phan7tom
Did people have bad skin (acne) as often as they do now before this century? Why do I never notice it in old photographs from the 1800s? answered by /u/colevintage
In an attempt to answer a question about how spicy Aztec food was, I discovered that chilis were used to clear "roughness of the face" which I think might be acne. You may find the post interesting.