Looks like you would need to add a column that indicates who the user is. Normally this would be the primary key of your "users" table (or whatever you call it). Then your query would be something like:
SELECT ticket_nbr, ticket_date, ticket_type, result
WHERE user_id = :user_id
ORDER BY ticket_date DESC
As far as the mechanics of doing so in PHP, it depends to some degree on which database extension you choose to use. For a MySQL database, my first recommendation would be PDO (for ease of porting to a different DBMS if ever needed), otherwise the MySQLi extension (not the deprecated MySQL extension). Then you have to decide if you're going to use object-oriented syntax or procedural syntax. If none of that makes any sense to you, you've got some reading to do.