Primary key on existing table?

This may be a silly question but I don't see any place where the
documentation explicitly addresses whether or not you can designate a
particular column as a primary key after the table is created.  I used
the "create table as " syntax to create a table with the same columns
as an original table, but I want to rename id column, make it a
serial, and designate it as a primary key.  Is it possible to do
this?  I've tried a number of things to do this and none of them have
worked.

Carol