Along with a good eye and steady nerves archers will benefit from stronger shoulder, back and arm muscles. Adding a proper strength training program to your archery fitness training is a great idea. As you get stronger it will allow you to use a bow with increased draw. This will lead to a better flight trajectory for the arrow. In will also help you maintain good balance and keep you steady as you aim, leading to better archery results. If you are a bow hunter it will help in many ways, both in the archery aspect as well as hiking and carrying large game. Strength training can also help you decrease the chance of joint and tendon injury that can develop from repeated shooting.
A good program of archery exercises does not take a lot of time to provide good muscle conditioning and strength gain results. For upper body conditioning exercises that work the upper back muscle (lats), chest muscles (pectoral) and shoulder muscles (deltoid) should be included. Specifically the upper back can be strengthened with lat put-downs, seated row and chin-ups (these are considered an advanced exercise) motions, The chest can be worked with push ups, bench press and chest fly exercises. Deltoid muscles are worked with overhead press and lateral raise motions. These can all be performed with free with free weights (dumbells and barbells) or weight machines. Most gyms will offer a wide variety of options for you to work these muscle groups.
A very important pont to keep in mind while weight training is to always use proper form by utilizing a slow and controlled motion and working through a full range of motion. It is also important to work with intensity by performing repetitions on each exercise until the muscles are fully fatigued. You can get very good results with just one or two sets per exercise and a couple of workouts per week. Your legs should not be neglected so you will want to include some squats, lunges or leg press exercises. Stronger legs will definitely help with your stabilization as you draw and shoot.
Remember you do not need to spend a lot of time on your strength training program but including it in your training will provide benefit to your archery. You will find that the task of drawing the bow, holding steady as you aim and performing shots repeatedly will be much easier. This will allow you to concentrate more on your aiming and technique leading to increased accuracy.