Caliban, the hunt is of two parts: First the search and then the kill. The first part is the more difficult, but a gun isn't necessary and seasons need not be considered.
Find any tract of land, public or private, away from any notably built-up area. Find a good "sittin' spot", where your shape isn't skylined and you have a view of an edge of woods and either an open field or lightly-covered brushy area. Go there about an hour before sundown, and just sit until dark. Think to yourself, "I am a rock." (or log) Do your best to imitate such, as in don't wiggle or twitch. Nothing wrong with taking a folding chair with arms. Mainly, you want the wind coming pretty much toward you from your viewing area in front--or have a cross wind.
It's amazing how many critters will be moving in that last hour or two of daylight, particularly when the moon is coming full. (Predators gotta work harder, then, so they start earlier.)
Another thing is to amble slowly in a wooded area, preferably with soft-soled boots. Look all around, take a few steps, stop and look all around. The trick is to glance down and figure your next few steps before you walk. That way you won't break twigs, and can continue looking around instead of at your feet. Slow, I said! Maybeso a few hundred yards an hour, or even less as a function of density and terrain.
It takes practice, just like being a mechanic, doctor or jeweler. Nobody was born an expert anything. Always remember that.
Some reading for the flavor of the outdoor world: Anything by Ernest Thompson Seton--although around 100 years old, they're timeless. Ruark's "The Old Man And The Boy" and "The Old Man's Boy Grows Older". They're timeless, as well. These books aren't really about "how to hunt" so much as give a feel for the whole thing.
, Art