It could be they're doing nothing. It could just be they've lucked out and have a naturally social, adventurious, anxiety-free child. Great for them, but not too helpful for the rest of us.
However, not all these cheerful tots are innately courageous. Many -- probably most -- of them have had to be taught the pain-free drop-off, and, very likely, have to be reminded every so often. (Why does a formerly chipper child suddenly become clingy? Sometimes there's a clear cause-and-effect, but most of the time it's just one of life's little mysteries.)
Often, the child makes the most fuss when it's the mother dropping them off. Many families choose to have daddy or a family friend drop the child off, and let the mother do the end-of-day pick-up. It's straightforward, and if it works for you, that's generally the simplest solution. However, maybe the child cries no matter who drops them off; maybe mom has no other option but to do the drop-off. Then what?
There are two schools of thought on this one (when are there not?). One has the parent staying to ease the child's transition. The other has the parent taking no more than a couple of minutes to make the transition. In one, the parent often comes into the room to play with the child. In the other, the parent stays firmly in the door.
There are pros and cons to each. You'll consider your preferences, your child's character, and your child's caregiver's input. I'm not going to get into the pros and cons of each right now. We'll skip past that and get to the point where, no matter which method has been used, the parent is about to leave.
(I am assuming here the child knows you're leaving. Do you sneak away when the child is occupied? Some people say you should never do this; it's unnerving to the child and will only make them more anxious the next day, when they'll be afraid to let you out of their sight. I say it depends on the child, and while it makes some kids anxious, with others it works like a charm. You may have to try before you know.)
You know what, though? No matter whether the parent has stayed for two minutes or two hours, when the child realizes that mommy is about to leave, they will almost certainly cry. If you've lingered in the hopes of a happy, smiling drop-off the very first day, you're almost certain to be disappointed.