If the lever touches the handlebars then you need a larger adjustment than you can do with the barrel adjuster (the silver bit just as the cable exits the lever on the handlebars). So you need to make the cable shorter.
To do that you need to undo he bolt where the cable meets the actual brake arms (just after the curved bit of metal), whilst holding the cable, then pull it through about half a centimetre and then re tighten the bolt. I usually untighten bolts by about what I call 1 and a half full turns, then I know to tighten it up by the same amount.
Then try the brakes and the levers should touch the handlebars hopefully.
That's probably not the best explanation, but I'm not a really technical person, but it should be a starting point, with the information you've been given above. There is more refining you can then do with the barrel adjuster.
Edit: what
@Ihatehills said above, that will teach me not to read to the end of the thread before replying.