I'm glad you've decided to start exercising again. I hope you worked everything out!
It's really up to you how long it takes to get ready. Obviously, if you haven't exercised in a while, it's smart to start out slow and work your way up, but it shouldn't take too long.
The concept of most training programs are all about starting slow and building gradually each week. There are places where you can spend money to get a specific program, let me know if that's something you want. I wouldn't consider myself a running expert, but I do think I can help you. I would recommend starting out with a low mileage (2-3 miles) where you run/walk to get started, until you feel comfortable running the entire 2-3 miles. Then you just slowly add a little more each week, trying to work up to around 7 miles, just so you feel comfortable that you can do it. Take it easy the week before the 10k to let your body rest. You can run 3-4x a week, either a Tuesday, Thursday, Saturday schedule or a Monday, Wednesday, Friday, Sunday schedule. Whatever you feel more comfortable with.
Make sure you get plenty of fluids and complex carbohydrates. Let me know if you need more help.