"Pursue your goals, but never lose sight of the reality of things." -Amy Suto
Always start your training off slow. When I first started running, I ran twice a week for one mile each. I was running a veeerrry slow 17 minute mile and often had to stop and rest. Now I can go six miles an hour, and I completed my first 10k without dying like I thought I would!
Once your body gets used to that, add mileage, not speed. Once you get to four workouts at 3-4 miles apiece, you can begin to focus on time and actually get into a legit half marathon training plan. But you have to build a certain amount of endurance before you can start doing interval sprints.
In any workout plan, cross training and weight lifting is a must to build muscles and protect against injuries.
Once you can run three miles fairly consistently, try a half marathon plan like this: http://www.halhigdon.com/halfmarathon/novice.htm
Best of luck!