If I was out on a long hike, and I wanted to shoot a bird for supper, is there a way to find out in a very short time whether or not that species is legally protected? Sometimes you can get in trouble for picking up a feather of some birds.
It's much easier to know what's not protected than to try to know what is protected. In most of the United States there are only a handful of birds you can legally hunt, and only during "season".
This is a general guideline, that can help you narrow it down and not waste time, but this does not replace picking up a DNR guide for your area. The easiest way to find the DNR guide is to google [your state] department of natural resources.
What you are left with is a small assortment of dove, pheasant, quail, etc. However even with legal game, there are often strict limits on when, where, and what you can kill. In most of the southeast for instance, killing a female turkey is a VERY expensive mistake.
This information is based on my experience in the United States.
You'll actually want to prepare before you go hiking:
Then, once hiking, if you see a bird not on your whitelist, just leave it be. This way saves a lot of problems, and legal consequences.