One of my pet peeves is when lettuce goes bad in a day or two after purchasing it. To ensure the longest shelf-life possible I always take these steps when cleaning and storing lettuce.
To start, I fill my salad spinner with ice cold water. Then submerge the lettuce and gently spin to remove dirt. Lift the strainer containing the lettuce out of the salad spinner and dump out the dirty water. Fill the spinner with another round of ice cold water then submerge the strainer again and gently spin. Drain the water and replace strainer in spinner and spin until as much water has been removed as possible.
Dump lettuce onto a kitchen towel on the counter and top with another kitchen towel. Gently hand dry. Place lettuce between sheets of paper towels and store in a large ziplock bag in the fridge. Replace paper towels daily to prolong shelf life of the lettuce. Depending on the variety of lettuce, it should last 4-6 days.