The hardest thing about starting to run is actually getting out of the front door. Your perception about what's going to happen may interfere with what actually will happen. There is a myth surrounding running, people assume that you have to have some kind of sporting gene to be able to run and that's just not true. Anyone can run given the right tools, put your trainers on and walk out of the door, set yourself a small goal of running between lamp posts, then walking, then run again. 10 mins is more than enough to start off with.
Slow it down...another myth that surrounds running is that you have to be fast. No you don't, in fact most runs should be run at a comfortable, talking pace and if you can't talk, slow it down even more, as long as one foot is off the ground at any one time you are running.
It's ok to walk, I am giving you permission to walk, everyone has to start somewhere and walking is the right thing to when you first start running.
Breath through your mouth, it's bigger than your nose airways so get the air in and out through the bigger airway of the mouth (see above; you have to talk with your mouth open).
Relax, nobody really cares what you look like, most people are too busy thinking about what they are having for dinner and if anyone does shout anything, just ignore them. Hold your head up high, not only will it make you look like a runner but it will give you a confidence boost and nobody knows if you've just finished a 20 mile run or a 10 min run/walk.