Fitness in archery is key to becoming a top performing archer and even at a lower level base fitness will dramatically improve your scores.
There are two main components of fitness in archery.
Good general fitness, especially cardio-vascular fitness, is really important in archery, archery tournaments can last all day and you need to be as strong on the last shot as you are on the first. At some competitions you will walk over 2 miles (3.5km) in a day. This is where most new archers struggle, archery is not a cardio-vascular sport but it is really important for improving scores.
Good stance and posture are essential to a good shot, core strength is important to maintaining good stance and posture throughout your shot and throughout a tournament.
There are specific exercises that have been developed for the core muscles that will allow the archer to build on their core strength. I would encourage all archers to visit the NHS site on posture which provides links to establishing good posture through core muscle exercises.
Archery Specific Fitness
Archery uses a lot of the upper body muscles, the key ones for shooting are the muscles in the back. When starting out you can use the archery warm-up exercises as a good way to start, check out this video of Team GM Olympian Naomi Folkard showing how it's done.
As you shoot more and develop you should start doing bow drills. The most basic form of bow drills is simply drawing the bow back to full draw, holding it and then relaxing. Start with 15 seconds at full draw and then 20 seconds rest, see how long you can repeat this for until you start losing your form (stop when your form starts to go, you don't want to practice bad form). Once you can do this easily start to increase the time at full draw, the aim is to get to 30 minutes of 30 seconds at full draw and 30 seconds rest on your full competition bow (WARNING: Do not try going straight into this, you are likely to injure yourself).