Depending on what kind of engine you have, there are numerous fuel delivery systems and we will go over a few here to see if you can find the problem.
On small lawn mower engine such as push and self-propelled units, the fuel is usually delivered by gravity to the carburetor. Anything that affects this gravity can cause no fuel to be delivered. Starting off the with the gas tank, you want to be sure that the fuel cap is venting properly. When you open it, is there an inrush of air? There should not be. Is the fuel strainer in the tank clogged up? Is the inline fuel filter clogged? Is there a clog in the fuel line itself?
If all of those things are fine, then that narrows things down to the carburetor. Something internally such as the needle and seat are stuck together and not letting fuel to flow.
On larger engines such as a riding lawn mower, there may be a fuel pump built into the system. As on the small engine, you want to start at the gas tank first and work your way down to the fuel pump. Then disconnect the fuel pump output side and crank the engine over. Have a catch can to catch the fuel that will squirt out. If fuel is coming out of the fuel pump, then the logical thing is that there is a problem with the carburetor.
Loose engine intake valve clearances can also cause a lack of fuel to enter the engine. If all else fails, check those valves to ensure that they are working as they should.