How to choose the best:
Honeydew

Touch

A good honeydew should be a tiny bit soft, with a nice textured skin.

Give your honeydew a little press with you finger on the end without a stem: it should be just a little bit soft.

Smooth skin and hard flesh are signs that it might not yet be fully ripened.

See

The best honeydews have skin that looks sort of dull — shiny skin is a sure sign of under-ripeness.

Smell

Give your honeydew a nice sniff at the end opposite the stem, where you should get a nice strong aroma. Anything too sweet is a sign that it might be a bit overripe.

This'll be your best sign for a primo melon.

Some more details:

How to clean

Do yourself a favor and give your melon a quick rinse in water with just a dash when of vinegar when you bring it home, to help avoid fruit flies later — especially if it'll be left out at room temperature. Just make sure to dry it off well after!

How to store

Once your melon is fully ripened, store it in the fridge for longest life.

If the melon needs to ripen it a bit more, you can leave it out for a day or two until its good and ready.

When it's in season

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.