Archery is sometimes viewed as a static sport compared to other sports such as football or snowboarding, but in reality it requires just as much physical training and conditioning as anything else. There is a huge difference between professional archers and hobbyists, and the reason the pros are so much more proficient is because of several reasons. Technique and equipment both play a huge part obviously, but physical training should never be overlooked. At your local archery range you'll probably find people that don't stretch, don't warm up, don't generally perform any exercise at home, and snack on mostly pizza, beer, and soda.
These people may be fairly good, but they will never become the best because they don't have the body and training to meet the physical requirements of professional competition. Archery is a sport that requires full control over your body and your bow while shooting. This means the entire body, not just the arms and shoulders.
First of all, a good stretching routine is absolutely critical to your ability to perform at your best. Archery places a lot of strain on the biceps, pectorals, shoulders, triceps, and fingers, so a proper stretching routine should focus on all of these areas. As you focus on those body parts, be careful not to neglect the legs, which are used for balance, and the core, or torso, which ties everything together.
Drawing a bow is hard work, and you need to be sure that your body is in top physical condition to be able to do this as effortlessly as possible. Overhead presses, bench presses, and arm curls focus on the upper body. The goal of physical training for archery is to increase lean muscle mass without necessarily adding excess bulk. Extremely bulky arms can get in the way. Compound exercises focus on several muscle groups at once and give a lean, complete strength that is ideal for archery. When you draw a bow, your fingers are tensed; your triceps are flexed to carry the force back from your biceps. You biceps are anchored by your shoulder. All of these muscles need to be able to work in tandem with each other at any given time.
Being able to draw a bow and fire perfectly once is great, but can you do it over and over again with the same exact precision every single time? Muscle endurance is just as important as tensile muscle strength when it comes to archery. Focus on your ability to complete a specific action multiple times without sacrificing quality of motion. One way to build this up is to run a routine where you time yourself for 5 minutes and see how many arrows you can fire in that time. Don't haphazardly toss off a bunch of shots, but instead focus on your range of motion and technique for every single shot.
Archery, despite common opinion, is just as physical as any other sport, and as such it requires physical discipline and training.