There are two little mini-games offered,
Dizzy Driving and
Acme Antics. Both are extremely simple and easy to understand.
Acme Antics is a simple action game where you control the road runner as he flees from the ever-present Coyote. You move between there lanes of road, avoiding the Coyote as you jump and duck past obstacles and picking up some birdseed along the way. The game is divided into discreet levels with the Coyote using nastier tricks each level.
Dizzy Driving is a little more complicated, but is basically just a very bare bones racing game. You can choose from any number of Looney Toons characters and go through either a single race or play Tournament mode. Tournament mode is the only thing in Looney Toons: Double Pack that even approaches something engaging. While the entire tournament process itself is far too long for a portable title (thankfully you can save), the offerings are fairly varied. You have your standard races, standard races with the added requirement of collecting all the flags on the course, and a last man standing battle race.