There are three basics the engine needs: Ignition, Compression, and Fuel.
The specifics can vary from model to model, and your Manage My Home profile did not list what model this might be, but there are some quick checks you can do to see if you have these three basics. I am assuming from your question that this is a multi-cylinder engine with a good battery and that it is just turning over and not firing at all, but even if that is not the case these basic checks can still help narrow down the source of the problem.
First, go back to the spark plugs. Remove the leads, or wires, that connect from the engine to the plugs. Remove the plugs and put them back in the leads. Now position the leads so the metal end of the plug is against the engine or another clean unpainted metal ground point. Keep your hands away from the plugs so you do not get shocked, and turn the key to the start position. Look for sparks at the ends of the Spark Plugs. Look careful as they might be hard to see in sunlight or other bright lights. If there is spark there then you have ignition, the first of the three basics. If not, you likely have an electrical problem that needs to be traced.
The engine should have been spinning over faster once the plugs were removed and you should hear air rushing out of the spark plug holes in puffs. You could even try putting a thumb or finger over each plug hole to see if the pressure pushes your finger off when turning over, just be careful not to touch the grounded plugs so you do not get shocked. If that all happens then you have the second ingredient, compression. If not then you may need a valve adjustment or may have a broken component inside the engine.
That leaves fuel. Check the tips of the plugs you just removed, if fuel is reaching the engine there should be some residue there and they should look somewhat wet. If you used your finger to check compression then you may even see some residue on your finger. If there is fuel here your problem may be old fuel or a timing issue. Try putting a small amount of good fuel through the Spark Plug holes and reinstall the new plugs, hook the lead wires back to them, and turn the key to start. If your problem is fuel related only, the engine should now try to start, or even run, until the fuel you put in is gone. That would indicate the fuel supply is being stopped in the fuel tank, fuel line, fuel filter, fuel pump, or carburetor. Some carburetors have a solenoid to stop the fuel supply when the key is off and a malfunction there could also be the problem.
Often there are troubleshooting tips in your
that might also help and reviewing the electrical schematics and parts illustrations on the
site can help.
Or, if you could submit a more detail question with a little more detail on when and how the issue occurs, and be sure to include a complete model number, we will do our best to help further here.