Every parent has this problem once or more in their children's lives...
Children, heck PEOPLE tell fibs at time mostly to keep themselves out of trouble or sometimes to make themselves look or seem better.
Since we are the authority figures we are the ones they tell the fib to because we are either the punishers or the ones they want to impress.
Depending on the age or morals of the child you can use lots of different ways to get to them. My son is very concerned about how I feel about his actions. I told him if I find out it's a lie it makes him look much worse and I can forgive the truth, no matter what it is MUCH more than a lie.
Like holycow said, PRAISE them for being honest. Let them know the repercussions for truth are much less than being dishonest.
It's actually a cycle. I remember knowing that a lie would blow up in my face with my parents, so I chose NOT to do the things that I knew I'd have to lie to them about. It kept me on the straight and narrow for many years! I'm hoping that my son feels the same but even if he doesn't, he knows without a doubt my views on dishonesty and the repercussions of a non truth.
God bless, and remember, you're not alone in this!
Robinrs