Positive reinforcement is rewarding your dog with food, praise, or toys after he performs the desired behavior you asked of him, such as sitting, lying down, shaking hands, etc.
When you teach a new behavior or trick, food is good to use because most dogs are food motivated, meaning they love treats, which makes it faster for the dog to learn because they do what they have to, to get the treat.
This also will make the dog more willing to repeat the behavior because he knows he'll get treats when he performs the appropriate exercise.
Typically it works, much better than negative reinforcement.
However, once the dog understands the exercise and performs it well, you should begin removing the food motivator.
In other words, don't give a treat after every performance.
Only give a treat every other performance and then break that up into different sequences so that your dog isn't getting a treat every time and not in any pattern.
Then continue to reduce the amount of treats given for that exercise until you stop using the food.
Replace the food with praise.
You can still use food from time to time, just not every time.
If you continue to always use food, your dog will quickly learn to only perform when he knows you have food.
They are smart! Timing is everything! The reward should be given immediately after your dog correctly performs the exercise.
This is where a marker is a very good tool.
A marker can be a clicker device, or you making a click noise with your mouth, or even you just saying the word "yes!" at the appropriate time.
The marker (sound) lets the dog know that he performed correctly.
Then you follow with the treat.
The marker actually becomes the most important part.
The click says, yes you did it and did it right, now a treat is coming.
Without the marker, your dog performs correctly and when you go to reward the behavior, you potentially fumble in your treat bag, your dog moves in anticipation and then you give the treat rewarding an incorrect position, such as sitting sideways or getting up from a down.
When training your dog, be sure everyone around your dog knows the commands you have taught.
Let's say you have a family member that wants your dog to lie down.
You taught your dog the simple command of "down".
You dog promptly complies.
You praise him.
Later your family member wants your dog to lie down, but not knowing what the command word is, says "Fluffy, come here and lie down right here".
Fluffy looks at your family member and slowly gives a little wag of the tail but doesn't move.
So your family member says "Come over here and sit so you can lie down".
Fluffy quickly leaves the room because the human has begun to speak in gibberish.
Be sure to let everyone know what your command words are and how to say them.
Don't let them confuse poor Fluffy.
You will notice in most of what I write about, I will use the word consistency a lot.
It is absolutely necessary in any training you do with your dog.
If you want consistent results, you have to be consistent in how you train.
Reward the behavior you want and never reward the behavior you don't want.
Happy positive training!