There's always more that can be said but you may find an older answer I wrote about reading instruction in the 1920s helpful. (UrAccountabilibuddy is my old handle.) I'm happy to answer any follow-up questions you may have!

Most questions about education in American need to be prefaced with a contextual reminder about the 10th Amendment before an answer can get into general patterns. Unfortunately, the nature of your question is such that getting to the patterns part is nearly impossible as any quality answer is tied up with the pupil's race, gender, class, disability status, and physical location in the United States.

The era you're asking about marks the beginning of the end of the "Schoolman." Despite being a female-dominated profession, the policies, regulations, and pedagogical guidance of school had (has) been mostly shaped by men, mostly white. The late 1800's and early 1900's saw the rise of an American professional class that was basically men talking to each other about how schools should work and then giving edicts to teachers. They did surveys of each other's schools, held conventions, and often engaged in battles of words and texts about whose approach was more effective and more efficient. To give you an example of what this looks like in context, a 1951 article in the The Elementary School Journal looked at validity of six "readability formulas" (ways to calculate how difficult a text is to read) and all six were developed by a man (with one woman co-author) during the era you're asking about. In other words, there was no one way to teach reading because no one really knew how learning to read worked on a physical, biological level. Psychologists in the era you're asking about were just beginning to wrestle with "disordered reading" and dyslexia. To be sure, virtually every adult who has worked with children throughout history had a general sense of how it works: expose a young person to lots of sounds and words; help them connect the sounds they hear to the marks that represent letters; the marks to words; the words to things they see, hear, feel, and experience in the world; and eh voila, you have a reader. It was the mushy stuff in the middle that we've only just begun to meaningfully understand.

The end of the 20th century saw the culmination of all of these disparate positions on reading instruction in what was known as the "Reading Wars." Unfortunately, it's still happening so to stay within the rules of this subreddit, it's worth stressing again that the answer to your question is tied up in the answers to the following:

• what gender is the child?
• What is their race or ethnicity?
• What religion is their family?
• How wealthy is the family?
• Is English the child's first language?
• How close do they live to a major city? To a university or normal college?

Meanwhile, the notion that reading and writing are linked together is also relatively modern. As one modern educator puts it, "reading is the inhale and writing is the exhale," but at the time you're asking about, it was entirely possible for someone to be a functional reader but unable to write. Likewise, there were those that felt reading, writing, and spelling were all different cognitive processes. So, again, we have to go back to the previous questions.

As an example, if the child in question is a recent immigrant who first learned a Cyrillic language, living in tenement housing around other children and adults who are not literate in the English language, odds are good they're learning very slowly during instruction at their pubic school. Their teacher was likely young, disconnected from the research around reading and using strategies her teachers used. (Unless the school was located near Teachers' College at Columbia University. Then the teacher likely had a graduate degree and reading instruction was carefully planned.) The instruction would most likely involve a teacher reading a sentence from a text and having children repeat it back. The children may or may not have a book of their own to reference. The teacher would likely spend a few minutes a day talking to each student to see if they can "read" the sentence or text under review (in many cases, children just repeated back what they memorized.) Which meant, writing instruction was dependent on access to disposable resources and available instruction time in the day. It's possible the child's family brought texts in their native language and acquired an English version of the same text, enabling children to do translations as a way to learn to read English, but this depended on their literacy levels in their native language. However, the world was literature rich through signs, newspapers, pamphlets, and tracts. It's less that they were methodically taught to read and write and more that they cobbled together the skills through a collection of experiences, instruction, and trial and error.

However, let's say, though, you're talking about white children attending school just outside Pittsburgh or Kansas City at one of the sprawling new grammar schools that would become the model for the wave of WPA schools to be built in the late 1930's. Odds are good a young person would learn to read via the basal method. (This approach likely also held for a young person from a family of means who could hire a tutor. Unless the family was from old money, in which case, the tutor likely used a classical approach which meant the child left the nursery knowing the alphabet and corresponding sounds, able to recite the spellings of dozens of words, and was then immersed in rich, complex texts from the moment they started working with their tutor. They learned Greek, Latin, and likely French or Russian while learning English and developed a fluency in multiple languages at once.)

Basal reading is the idea of daily, systematic instruction and was the philosophy behind the McGuffey Readers popular in America from their first edition in 1836. The general idea was that learning to read required a sequence of skill development. The young person would learn harder and harder lists of words, sound combinations, and English rules until one day, they could read anything put in front of them. The approach is generally described as "whole-part-whole." (Reading whole words, deconstructing to learn the parts, then reassembling into familiar and new words.) This was a contrast to the so-called "word method" which required students memorize lists of words to prepare for those words in texts and was just "whole." And before that, there was the Alphabet Method, which was just "part." Basal reading instruction usually went together with writing instruction - as students were learning about "cat", they would write "c-a-t" and then "f-l-a-t", so learning the mechanics of writing happened alongside the mechanics of reading.

So, to wrap all of this up - it depends. It depends on the child's demographics, their parents' philosophy around education, their teacher or tutor's philosophy and which schoolmen were popular when the child was 4 or 5.