There's a scene in the 1980's television sitcom The Golden Girls where the ladies find themselves arguing at the supermarket over the right way to select a ripe cantaloupe. Dorothy said the way to choose a melon was to smell the tip. Blanche's "Southern method" involved giving the melon a thump. Rose's method, the "farm method," involved pulling out a pocketknife and cutting a piece out of each melon and sampling them all until a good one was found.

Blanche and Dorothy were both right to an extent. There are several steps to picking out a ripe melon.

Choose a melon that seems heavy for its size and does not have bruises or soft spots.
Tap the melon with the palm of your hand. If you hear a hollow sound, it's passed the first test.
Next, push your fingers on the round section where the vine was attached. It should be slightly soft and fragrant.

On melons such as cantaloupe and muskmelons, the rind underneath the net-like texture should be yellow or cream colored, not green. Honeydews should be pale yellow to light lemon in color, not greenish.