Basic fitness starts with cardio fitness. The cardiovascular system is the circulatory system; heart, lungs and blood vessels. As far as sports go, this is the fuel supply system for muscles; it takes in oxygen, transports it to the muscles together with the glucose you actually 'burn', and shifts the waste products - lactic acid, or lactate, and carbon dioxide - away.

For archery, you need adequate oxygen and energy supply, and effective waste product removal - particularly lactate removal. Low heart rate is a plus.

Cardiovascular training is basically whole-body exercise, typically for a minimum of 20 minutes - aerobic conditioning. There's an outline of the basics here, and some typical exercises here. Check out fitness sites on the web for detailed info and some personalised training schemes.

Muscles are what makes your bones move. Specific muscles do specific jobs in any sport, and archery is no exception. More, specific use means specific training (see  principles of training). So you need to know which muscles work for archery. Muscle use in archery is described here.

Training for muscles involves overloading the right muscles in the right way. Strength development needs heavy loads for a short time; endurance for muscles means light loads for many repetitions. Recommended training for archery is typically general 'toning', involving modest loads for 10-20 repetitions. Some useful exercises that work for archery are described .

Flexibility is important for range of movement and injury prevention in most sports. In archery, flexibility demands are modest but real; you need to get into the best mechanical position to control the bow, and that needs to be comfortable. Another issue is warm-up; it does help to get mobile and stay mobile before and during a shoot, and light stretching is needed to do that. Finally, if you're training muscles for strength or endurance, you should be warming up and stretching first.

Recommended flexibility exercises for archery are modest, and unsurprisingly geared towards upper body mobility. There's a selection of stretches here that cover the main requirements for archery. Field archers would do well to pay a particular attention to torso flexibility as well; good form at strange shooting angles demands flexibility in the waist and lower back.

A recent caveat; stretching, particularly static stretching, may not be the best thing for warming up; see  here for some more technical comment on that.