Protein?

It's not so much the protein as it is the amino acids. Amino acids are the building blocks of protein and if even ONE is missing, then there can be problems. Also, the quality of protein is important because it needs to be readily digestable in order for the available amino acids to be utilized. From the essential amino acids, which must be provided by the diet, the body can synthesize all other needed non-essential amino acids.
 
As far as the % protein, that will depend on the quality of proteins available in the diet and the AA available, but approximately 18 - 22 % is suggested for adult dogs in good health. and from 22 - 28% (if I remember correctly) for growing puppies.

How do you know what kind of amino acids are in a food?

You need to know what ingredients contain the EAA's. For instance, some fish are deficient in methionine and milk protein (casiein) is weak in arginine.
 
The ten EAA'a are:
 
arginine, histidine, isoleucine, leucine, lysine, methionine + cysteine, phenylalanine+ tyrosine, threonine, tryptophan, valine.
 
Most animal proteins contain reasonable amounts of EAA, but some can be deficient. That's why it's good to balance the protein sources and some use of plant proteins complement any deficits. Remember that the quality of the protein source (be it plant or animal) will determine the total % of crude protein.
 
Crude protein listed on the bag is basically just a way of measuring the nitrogen content in the food, because all protein breaks down into nitrogen and excess is eliminated through the kidneys.