Begin by familiarizing yourself with your snow blower's owner's manual, particularly anything related to the carburetor. If you no longer have the manual, attempt to find it online or obtain a new copy from the manufacturer. You will want to know what you are doing before you take your snow blower apart.
Using the screwdriver, remove everything necessary to get at and remove your carburetor. Specific actions will depend on your model, which is where the owner's manual can be useful. While you are removing parts, be sure to use a digital camera to carefully document all of your actions so that you can put the snow blower back together when you are done.
Submerge the removed carburetor in liquid carburetor cleaner. Allow the carburetor to soak for about three hours to remove all impurities. After soaking, rinse the carburetor off with water.
Clean out all of the small holes in the carburetor using the copper wire. This will remove any tarnish that has built up in the holes. Be very careful to clean out all of them.
After using the wire, use compressed air to blow any leftover tarnish out of the holes. Again, be sure to apply the air to each of the holes.
Using the carburetor kit, reattach the carburetor to the snow blower. Make sure that everything is just like it was before you touched it. Be sure to carefully review the pictures that you took while disassembling it, as well as the owner's manual.
If you are still having problems or experience any serious issues, take your snow blower to a local repair shop. It is worth the investment to avoid seriously damaging your snow blower.