If you are new to archery, don’t just buy a bow off the shelf. Go to an archery pro shop and get a bow properly fitted to you by an expert. You’ll start off with the correct pull weight, draw length and arrows matched to the bow. Before you buy, test-shoot both recurve and compound bows so that you understand the differences.
When shooting, avoid anything that might get caught in the bowstring such as loose clothing, neck wear, dangle-earrings, long hair, etc.
Successful archery is all about consistency*.
Stance –Your feet should be comfortably spread for stability, side-facing to the target.
Grip - Your grip on the bow should be relaxed, somewhat loose, do not "clench" it. Keep your bow arm straight, don't let your wrist bend inward. Wrist guards are optional.
Draw - Select an anchor point for your string-drawing hand. Some rest their knuckle against their cheekbone or jaw, others draw so that the string touches their nose, I anchor with the string on my chin; you may have a different anchor point. The goal is to figure out what feels right and works best for you and stick to it. A consistent anchor point is the most important step toward accurate bowmanship.
If you are using a recurve bow and no mechanical trigger, notch your arrow below the nocking point and wear a 3-finger archery glove or archer's tab. Draw only with the tips of your fingers, just short of the first joint. Grasp the string with one finger above and two below the arrow nock.
Sight picture - Whether using a pin-and-peep sight or just aiming instinctively, work to get the exact same sight picture every time. Focus on your target and exclude all other thoughts. The objective is to consistently group your shots close together (regardless whether you're hitting the bull's eye). Then you can work to adjust your aim up, down, left or right.
To adjust your bowsight: Aim at the bullseye and shoot as many arrows as it takes to establish a consistent pattern. If your arrows tend to group low, lower your sight pins; if they group left, move your sight pins to the left, etc. It’s best to zero in at very short range such as 10 yards then again at 20 or 30 yards.
Release - Again, whether using a mechanical release or just your fingers, strive for a smooth release, avoid jerking the string. Never release the loaded bowstring without an arrow nocked - it can do severe damage to the bow.
Follow-through – Maintain your stance, hold your anchor point and keep your bow in the shooting position until you hear the arrow hit the target. To lessen muscle fatigue, give yourself time between shots.
*The only way to achieve consistency is practice. (Then go practice some more!)