Start in Your Own Backyard
In order to begin gathering wild edibles, you must first learn to identify plants, whether edible or not, as positive identification is an essential foraging practice. Luckily, there is no better place to get started with plant identification than where you live. Chances are there are some plants, shrubs and trees growing near your home. Get to know them. (I'd be willing to bet that some of those plants have edible parts.)
Start by learning to identify the trees who live near you. Just pick the five most common species. Borrow a good tree book if you don't have one, or ask a knowledgeable friend for help. Similarly, learn five wild shrubs. Then, five herbaceous (non-woody) plants -- Newcomb's Wildflower Guide is a great resource to help with this. Learning to identify these fifteen species will go a long way toward helping you develop a discerning eye, but don't stop there. Get to know all of the common plants of your yard and neighborhood. At this point, I recommend checking your identification skills with a forager or plant expert in your area.
Once you are certain of your ability to accurately identify plants, consult an experienced forager and/or a variety of trusty foraging books (I highly recommend Samuel Thayer's books) and slowly but surely add to your wild food repertoire.