Welcome to the Forum!
There are a number of ways of doing this. On of the more common methods is to fix a braided loop (often come with lines or can be bought from a shop) onto the end of the fly line by threading the fly line inside the braided line.. A small rubber stopper is then super-glued over the braided line to securely fix this onto the fly line.
Then, you tie the backing onto the braided loop and, hey presto, fly line and backing are connected together.
See here also as I sometimes do similar...
http://www.flymartonline.com/article213.html
and another that shows you a bunch of other knots....
http://solutions.3m.com/3MContentRet...ersion=current.
best of luck and welcome to the greatest sport in the world
Ben