Good for you! First, and most important thing, is to get some good running shoes. Ideally, go to a specialist running shop rather than a chain if you can, as they will be able to recommend something suited to your needs rather than a fashion item 🙂
If you haven't run before then start slowly and try not to overdo things. A good way to start is to run a little, then walk a little - many people start off running to the next lamppost then walking to the one after. Soon you will be able to run two lampposts and walk one, and so on until you are running non-stop.
Run with a friend if you can as that can help motivate you. It can be a good idea to walk a route that you think you would like to run so you are familiar with it and can get an idea for distance.
I try and eat/inject 90 mins before, but in any event you should test before setting out and when you get back so you can see how your BG reacts.
There are lots of 10k training schedules around, so have a google and pick one that you think will be suitable. Let us know if you have any questions, and good luck!