First off, this is a excellent goal. 5k's (3.1 mile races) are a great way to give yourself a boost of enthusiasm for your new hobby and get to know other runners in your area. I wager that I've done close to 50 5k's over the years, and I still enjoy doing them.
If you've just started running and are following something like what I recommend in Running FAQ 1, you are probably already covering between 1-1.5 miles every time you run. Since your goal is to conquer a set distance, you'll need to find out just how far you have to go to be able to complete 3.1 miles.
Measure out a 1 mile course with a tool like MapMyRun. If you are running on a trail, find a park map or something of that nature that you can guess'timate off of. Once you have your course, start by running the length of time of your typical jog on your measured course and confirm how far you are actually making it on any normal run. This is your baseline distance.
On your next workout, run 2 minutes past that point. Why 2 minutes? Because I said so. Why not say something like "run an extra 200 yards"? Do you want to eyeball 200 yards at the end of a run?
Let's say you ran exactly 1 mile on your baseline test. The next run should be 1 mile (one complete course) and 2 minutes. Use a landmark (tree, mailbox, street lamp) to remember this middle finish point. On your next run, run 2 minutes past that point, and so on until you reach 3 miles.
As you may have realized, this means some of your runs will end a bit out from where you started. Walking is a great way to cool down and ease out of a workout. Eventually you will switch from walking back to the start to walking the rest of the course and completing another mile.
Add 2 minutes until you get can complete 3 miles. Complete 3 miles at least twice before your race so you aren't worried about being able to do it on race day. This will also give you the confidence to turn on the juice coming into the finish and sprint past that snarky neighbor of yours.
Feel free to post questions if you have any.