Congratulations on deciding to run your first 10K. The 10K training program I'm going to describe will allow you to do more than finish; you'll run strong.
Build up your running to least three or four miles at a time, three to four days a week. (Four to six days would probably be better, but it's not necessary if you have time constraints.)
Gradually increase the distance of your longest run by one mile each week until you reach eight to 10 miles. Do this run at a slow pace roughly one to two minutes per mile slower than your normal training run so you can cover the distance comfortably.
Every third week during your long-run buildup, try a 5K or 8K race instead of the long run to get yourself in "race mode."
Add one day of speedwork to your schedule each week. Find a track or level trail and, for your first speed session, start with 10 to 15 minutes of easy running followed by two 90-second intervals of hard running. Do these repeats significantly faster than your training pace, but don't sprint them. Jog for two minutes after each repeat. If you don't feel recovered after two minutes of easy running, you pushed too hard. Afterward, cool down with 10 minutes of easy jogging.
Increase this workout by one 90-second repeat each week for three weeks, but on the fourth week, drop the intervals back by one. Continue this buildup until you reach 10 to 12 repeats. For example: week 1: 2 x 90 seconds; week 2: 3 x 90 seconds; week 3: 4 x 90 seconds; week 4: 3 x 90 seconds; week 5: 4 x 90 seconds; week 6: 5 x 90 seconds; week 7: 4 x 90 seconds, etc.
Keep your other runs as they have been. They'll be your recovery. Also, schedule a rest day after both the long run and the speed session. Finally, the week before your race, cut your mileage by about 50 percent and skip the speed workout.
Good luck!10K Race.