Remember that native English speakers learn to speak the language before going to school and before learning the alphabet, so in that sense it is learned by learning the sounds.  Later in pre-school or Kindergarten, usually the alphabet and the sounds each letter makes are taught first, so that written words can begin to be recognized. Then, as the children are taught to write and to spell,  the most common words are taught to be recognized as whole words and some phonics are also taught so that new words can be sounded out. 

What is taught in school is primarily spelling, grammar, and some more advanced vocubulary.  Most speaking ability is taught by families at home.

It's hard to generalize about the United States because educational policy really isn't centralized. There are big difference between the fifty states, and within each state there is a great deal of local control.

As far as I know, the majority of schools--including the ones my children went to in the 1980s and the school I went to in the 1950s--use a mixture of "sight-reading" and "phonics."

We were taught to use sight-reading as the primary method--learning words as visual wholes--with phonics as a kind of memory aid or back-up. If we weren't sure of a word by sight, we were told to "sound it out."

I agree with Susan.  Despite school, the bulk of learning occurs at home. I was taught to read by my parents before I attended school.  

I also agree with Dan Smith, that the educational system in the US varies widely.  Even in one city there may be many different types of schools for children of the same age.

In general, I think that we are taught to "sound it out" and to recognize certain words.  There are many words that sound nothing like the way they are spelled so you need to memorize as well.