Copying a column from one table to another

Suppose I have a table "people" like this;

Name   Age
David    25
Simon   19

and a table "occupations" like this:

Name  Occupation
David  Teacher
Simon  Student

"Name", "Age", and "Occupation" are just the column names, not data.
The names are unique and one-to-one, i.e. if there's a David in one
table then there's exactly one David in each.

I know that if I want to display

David  25  Teacher
Simon 19  Student

I can use something like

select people.name, age, occupation from people, occupations where
people.name=occupations.name

But, what I would like to know is, how can I copy the column
"occupation" to the table "people"?  That is, I want to create a new
column people.occupation and populated it from occupations.occupation.
Feel free to point me to a relevant section of the documentation.

David