Guys with guitars in the Mississippi Delta playing the blues only really started happening in the very late 19th century (and was likely somewhat later in Chicago, likely with the Great Migration - the urban blues was quite different, and less acoustic-guitar based and more band-based). This was often due to the rise of things like the Sears mail order catalog (which grew to prominence in the early 1890s) advertising acoustic guitars that were affordable for people with the earning capacity of rural sharecroppers who were oppressed by a dominant ethnicity who had within living memory enslaved them. For a pre-electric time period, such guitars were quite loud and thus suitable for being used as dance music accompaniment. Before that the dominant musical instrument among African Americans who aimed to do similar things to blues guitarists was probably the banjo. This was an instrument originally based on an African instrument, the idea of which transported across to America with slavery. However, across the 19th century, the banjo acquired unpleasant associations thanks to the blackface minstrelsy which very commonly used banjos as musical accompaniment (blackface minstrelsy, shall we say, didn't go down enormously well with African-Americans after the end of slavery, what with it being enormously racist against them.)

The existence of the banjo suggests the existence of an inherited oral tradition amongst such people about how to tune multi-stringed instruments and how to chord them, which could be relatively easily transferred to the new-fangled Spanish-style acoustic guitars that were becoming popular in the late 19th century in America, with some trial and error. As to how they learned, quite often musicians started out playing 'bo diddleys' or 'diddley bows', which were basically string attached to a bendable piece of wood, and which thus could make different tones by changing the tautness of the setup.

Up Jumped The Devil by Conforth and Wardlow is an excellent historical study of the blues singer/guitarist Robert Johnson; we likely have much more detail about Johnson than most other bluesmen of the initial era of popular recordings of acoustic rural blues (the 1920s and 1930s) thanks to the mythology and aura around Johnson, which motivated decades of research by Wardlow. As such he's a good example, though likely atypical in some ways.

Johnson, who was active as a recording artist in the mid-1930s, was literate due to a few years of a decent education in a relatively progressive part of Memphis during most of his primary school years. This was probably not the case for most other blues guitarists in the more rural parts of Mississippi Delta, however, where African-American children were not educated with any enthusiasm (as education was seen as getting in the way of putting them to work in what was a fairly hard scrabble existence). Johnson thus would have been able to read the instructions that came with tuning a guitar etc, though he likely didn't read sheet music and thus would have learned skills through practice rather than literary study.

Apparently a young Robert Johnson was obsessed with a diddley bow, and noticing this Robert's older half-sister Carrie at one point helped Robert put together a homemade 'cigar box guitar' with four strings (which was of course cheaper to make than even the cheap guitars in the Sears catalog). By 1927, Johnson had accumulated enough money and ambition to buy a store-bought guitar - an old second-hand guitar missing two strings he found in a general store.

From there, Robert Johnson began hanging around with an older blues guitarist, Willie Brown (who had played live with Son House and Charley Patton), who very likely taught him the rudiments of the style; basic blues guitar chording isn't that hard, and can be mastered relatively easily - there's only three chords after all. For Johnson, there was a period when he was famously considered by the likes of Son House as being a very average guitarist; Johnson then left town in order to learn some much more advanced techniques from a blues guitarist, Ike Zimmerman (who despite the name was African-American) who he essentially apprenticed with for a period of six-ish months. When he came back from his 'apprenticeship' with Zimmerman, he had a set of much more advanced techniques which allowed him to have simultaneous chording and soloing, and which made him stand out from the crowd of blues guitarists in the era.