Harvest when the gourd is mature. This is when the vine begins to turn brown where it meets the gourd. Cut the stem 3" from the gourd body. Dip them in either a bleach or borax solution. Handle the gourds carefully to prevent bruising, and put them in an airy place - NOT in a basement , garage, or tightly enclosed space. I have found that putting pallets outside our barn,and storing the gourds on these works quite well. I stand the gourds up in a single layer, taking care not to double stack them. Double stacking is tempting, but can lead to stem breakage, as well as scratching and bruising of the gourds skin. Freezing will not hurt a mature gourd, but WILL shrivel up the non-mature gourds. Non-mature gourds just throw away - they will be no good to use, and will rot.
If you leave your gourds uncut on the vines, after they are mature, and are ready to harvest, the cucumber beetles tend to eat the outer shell, and burrow into the gourd. This causes them rot, and if they don't, it mars their outer shell.