That is a screw on free hub, not a free wheel, so you don't need a chain whip to get it off. Instead you need a freewheel removal tool to match your freehub. From the photo, the brand looks like "starlit" which google suggests is a Chinese bicycle factory. If you are lucky then a shimano freewheel removal tool will fit. If not, you may have a difficult and expensive search for the correct tool. I strongly recommend that you take it to the bike shop so that they can tell you what tool you need.
After that it should be fairly straightforward. This article explains the details.
http://sheldonbrown.com/cone-adjustment.html
In summary, you will need a pair of thin 15mm spanners to lossen the bearings, some 1/4 inch ball bearings, and some new grease, (and if you can find one, a grease gun)