When training your puppy, "down" means lie down on the ground immediately, without hesitation, doubt, or delay. Many people have never seen what this looks like and, as in all things, it is hard to get somewhere you don't have the mental address for. To give you a picture in your head, here is my dog, Pip, demo'ing this down on a walk we took today. This was the first round; no editing, no retakes.
How do you get here to this sort of immediate response that happens reliably, on or off leash, close or at a distance, treat in hand or no? Here are the basic steps:
Read My Smart Puppy - all the games and exercises are in this book. It is the handbook for MySmartPuppy.com and will help you and your puppy in many ways.
Teach The Guided Down. It is critical you be able to calmly, kindly and consistently help your puppy or dog respond each and every time if your goal is for your dog to respond consistently each and every time. Your dog can never be more consistent, more immediate or more clear than you are.
Say it, do it. It is as complex and as simple as that. Once you say it, the dog either does it or you help him do it in a relaxed, easy way. Those are the options. Pausing or repeating will teach pausing and repeating. Giving up will teach giving up. Becoming stressed will teach becoming stressed.
Listen to The My Smart Puppy Minute: Getting to Good to learn how to help your dog succeed. Becoming success-focused takes the stress out of the process for both you and your puppy/dog.
Remember, your dog is doing the very best he can. He is not stubborn or spiteful, stupid or confrontational, he simply doesn't understand what you want yet. So, help him. Help him get it right and soon, he'll get it right.
Have fun. It's important! It's important for your dog's and your attitude. We all do what it is fun to do - make it fun!
Those are the puppy training building blocks. For customized guidance, stop by the My Smart Puppy Forums. The forums are free, they are moderated, and they are there to help people like you create success with dogs like yours.