Check the fuel level in your two-cycle engine if it will not start. If there is gasoline that has been sitting inside the fuel tank longer than two or three months, remove the gas cap and dump it out. Add the appropriate amount of two-cycle oil to one gallon of gas. Mix it up well in the gas can, then add it to the tank. Your specific product instructions will tell you how much oil to mix with one gallon of gasoline.
Remove the air-filter cover and check the air filter if the engine has trouble starting or continuing to run once it has started. If it is dirty, either tap it lightly on the ground to clean it or replace it with a fresh filter. How to remove the filter cover will vary with different engines and products. Either unscrew the cover with a screwdriver, or, if there are metal or plastic clasps instead, flip them up for removal.
Inspect the fuel lines while the air-filter cover is off. They run from the gas tank to the carburetor, which is located underneath the air filter on most two-cycle engines. If they are cracked, remove them with pliers and replace them with new ones.
Check the primer bulb as you are inspecting the fuel lines. The primer bulb is the rubber bulb that is pressed to circulate gas from the tank to the carburetor. To replace a cracked primer bulb, pry the assembly out with a flat-head screwdriver and snap a new one in.
Remove the two-cycle engine's spark plug wire and take off the plug with a spark-plug wrench. Replace it with a new spark plug.