Watch for the melon's skin under the outer webbing to start turning yellowish or tan. You'll also see this color develop on the underside of the fruit. As it ripens, the whole melon (Cucumis) will become one color. If the color under the webbing is still green, it's not ready to pick.
Melons will ripen indoors if you pick them when immature (as commercial growers do), but they won't taste as good as vine-ripened fruit. Ripe cantaloupes give you another clue that they're ready to pick-the stem end separates easily from the vine. If the color looks promising for ripeness, give the fruit a little tug. If it's ripe, the stem of the fruit will release with little effort.