All internal combustion engines need three things to operate (air, heat or spark, fuel). Check to see if you have all of these things, a clean air filter with a clear path to the carburetor, spark at the end of the plug wire (this can be checked by using a screwdriver inserted into the plug wire end and holding it close to a metal grounded surface), and fuel to the carburetor (check to see if you have fuel at the fuel line going into the carb or an easier test is to spray a small ammount of carb cleaner into the throat of the carb just before cranking, if it starts and runs you have a fuel supply problem then check backwards to find the blockage (pinched fuel line, plugged fuel filter, bad fuel pump ect).

If no spark at the plug wire check all connections at electrical terminals under hood and at switches for parking brake, belt engagment (PTO) ect..

Usually if something runs and then just dies suddenly there is an obvious problem, your powers of observation will help you the most. Look at anything that looks out of place.