Falling up on painkiller's advice.
First labor (forget about parts) at a bike shop to make the swap is probably more than you paid for the bike.
It is an easy swap - if you have the tools and follow Shimano's installation instructions. You can download the instructions from Shimano's Techdocs site - you need to know the model number of the shifters.
The STI shifters and your freewheel(or cassette) MUST have the same number of speeds/cogs. If they do not match, they will not work together, and one or the other will have to be replaced.
You will need cable cutters for high strength steel cables; like these: http://www.amazon.com/Pedros-131839-Bicycle-Cable-Cutter/dp/B000IZEH3S/
there are more expensive ones out there. I have this one, and it does a good job. If you try to use standard diagonal cutters like these: http://www.amazon.com/Stanley-84-105-6-Inch-Diagonal-Cutting/dp/B0001IW89W/
you will ruin the tool and get a very hard to work with cut.
Materials/parts you will need:
* new derailleur cables - unless the shifters are new and came with cables.
* derailleur cable housing.
* new handle bar grips.
Other tools you will need:
* metric wrenches; usually 8, 9 and/or 10mm
* metric hex key; usually 4, 5 and/or 6mm
* #2 Philips screw driver
* 3/16 or 4.5mm flat bladed screw driver
It is also nice to have a bike stand or something hang your bike on. I use a spare tire bike rack on the back of our Jeep: http://www.amazon.com/Allen-Sports-Deluxe-3-Bike-Spare/dp/B000ELSSWW/