The advice given so far is a mix of good and bad.

The good: Replace your cables and housing

The bad: Cutting is your best/only option

The reality: You most likely don't have to cut anything.

The how To:
1. Take a pliers and pull the metal end cap off each of the cables.
2. Find the anchor bolts on the brake calipers and the derailleurs.
3. Loosen the anchor bolts.
4. Pull/push the cables free of the brake levers and the shift levers.

Park Tools website should have directions for replacing or installing cables. OR you can purchase a decent repair guide. There is a good one published by Bicycling Magazine called "Bicycling Magazine's Complete Guide to Maintenance and Repair".

The only time you would need to cut the cable and housing during removal is if the two are badly rusted together.

-j