How do I add a foreign key to an existing SQLite table?

You can't.

Although the SQL-92 syntax to add a foreign key to your table would be as follows:

ALTER TABLE child ADD CONSTRAINT fk_child_parent
                  FOREIGN KEY (parent_id) 
                  REFERENCES parent(id);

SQLite doesn't support the ADD CONSTRAINT variant of the ALTER TABLE command (sqlite.org: SQL Features That SQLite Does Not Implement).

Therefore, the only way to add a foreign key in sqlite 3.6.1 is during CREATE TABLE as follows:

CREATE TABLE child ( 
    id           INTEGER PRIMARY KEY, 
    parent_id    INTEGER, 
    description  TEXT,
    FOREIGN KEY (parent_id) REFERENCES parent(id)
);

Unfortunately you will have to save the existing data to a temporary table, drop the old table, create the new table with the FK constraint, then copy the data back in from the temporary table. (sqlite.org - FAQ: Q11)

You can add the constraint if you alter table and add the column that uses the constraint.

First, create table without the parent_id:

CREATE TABLE child( 
  id INTEGER PRIMARY KEY,  
  description TEXT);

Then, alter table:

ALTER TABLE child ADD COLUMN parent_id INTEGER REFERENCES parent(id);