The key to keeping cookies fresh and soft is to seal them in an airtight container, like a resealable freezer bag. And here's a nifty little trick: add a piece of bread to the bag.
You might think that the bread trick works because the cookies absorb moisture from the bread. But what's actually happening is that the extra moisture from the bread creates a humidity level inside the bag that slows down the moisture loss from the cookies.
It's like going out on a hot, humid day. The extra humidity in the air makes you feel hotter because you can't perspire fast enough to cool yourself down. It's the same with the bag of cookies. The air inside the bag is already so saturated that there's no room to add more. So the moisture in the cookies stays in the cookies.
Some folks recommend using flour tortillas, especially if you're shipping your cookies in a round tin. The tortilla works the same way as the bread, but since they're round and flat, you can stack the cookies with a tortilla between each layer.