Info for replacing a shift cable housing
I would suggest replacing the inner as well as all the outers. If the inner is frayed at all, you will not be able to rethread it. The benefits of a new cable are much better shifting, to the point cables are considered a consumable by many riders - just like tires and brake pads.  

Shifter cables are very generic and cheap - as low as $5 online for a set.

You will also need a cable cutter. Dedicated bicycles ones make the job fast and tidy. You can use heavy duty wire cutters, but needs more care and is less successful get tidy and fray free cuts. If you don't have access to a decent cutter, you could buy one for about $25. If you plan this to be a once only, the LBS will install a new cable cheaper than buying the tool.