Find the book "Diet for a Small Planet." It just came out with a 20th anniversary edition not long ago. It's not too hard to find in libraries, too. The book explains the whole science of complimentary protein and makes it simple.
Lots of foods, of both plant and animal origin, have protein. But what we need is not just "protein" in general, but particular proportions of amino acids, the building blocks of proteins. Proteins are broken down in our digestive systems into amino acids, which are then absorbed.
Most of the proteins we get from plant foods are rich in some crucial amino acids and poor in others. By eating several different plant foods, each of which is rich in a different amino acid, the total amino acid "soup" in your digestive system will have the right balance.
It sounds complicated, but fortunately it comes down to a few simple combinations, such as whole grains plus beans or tofu, or whole grains plus sunflower seeds -- mixes you see in a lot of "peasant" foods and ethnic foods. You don't have to get both at exactly the same time, either. So long as you are getting a mix of plant protein sources over the day, you'll get the amino acid mix that you need.