How did Scout learn to read and write ?

Scout learned to read while sitting in her father's lap.

Now that I was compelled to think about it, reading was something that just came to me, as learning to fasten the seat of my union suit without looking around, or achieving two bows from a snarl of shoelaces. I could not remember when the lines above Atticus’s moving finger separated into words, but I had stared at them all the evenings in my memory, listening to the news of the day, Bills to Be Enacted into Laws, the diaries of Lorenzo Dow — anything Atticus happened to be reading when I crawled into his lap every night. Until I feared I would lose it, I never loved to read. One does not love breathing.

Calpurnia taught Scout to write.

Miss Caroline also got made at me for knowing how to write!! Calpurnia was to blame for that!! On rainy days she would have me sit and copy out a chapter of the Bible.