You form action attribute should point to a form processing script which will carry out the update to the database.
To identify which row in the table to update, you may want to select the row ID value in the initial query, and put that into the value attribute of the option tag.
This way the processing script can get the ID from the POST array and give it to the update query.
The actual submit button isn’t the hard part, it’s just a standard form submit input.