A good training program for running a 10K is the "Couch to 10K" program. It involves running three days per week and intervals of walking and running periods. The running periods increase over time to build stamina. It is designed for beginners but can be used at any fitness level.
Another good 10K running training program for beginners is a six-week program that requires 16 to 24 miles per week with five days of running and two rest days. It has short intervals of fast running with slow pickups.
For intermediate runners, a good 10K running program is another six-week program with 20 to 26 miles per week, five running days and two resting days.
For expert runners, a good training program involves 14 to 39 miles per week for six weeks. It has one day of rest and six days of running.