Is it a four stroke or two stroke?. Asuming it's a four stroke The oil sits in the crankcase, and you don't add oil to the mix. You put standard or normal petrol in the petrol tank. The problem can be either petrol related or ignition related. Always do the easy checks first. Ignition, remove the spark plug and wedge to the metal frame, well away from the cylinder hole it screws into. If you can't find a suitable place get a single insulated wire lead and bare about 1'' from each end. Attach one end to a bolt or screw on the frame and wrap the other bare end around the body of the plug, near the treaded end. Clip the high tension lead onto the nut at the end of the plug, making sure the nut is tight on the plug. Pull the start cord as rapidly as you can. The engine will turn easily without the plug in place. You should see a fat blue spark about five times or so and hear a crackle with each spark. No spark means no ignition. Next the spark plug itself could be cracked inside and making poor contact, so change the plug for a new one and repeat above. If you get sparking, that was the problem, if not, you go to stage 2. This involves removing the cowl and flywheel and may void your warranty, so if you are not getting a good spark, take the machine to the dealer and demand repairs or a new one under warranty, before removing the flywheel. Suppose, you did get a good and regular spark its time to check the timing. put your finger just inside the plughole and very very gently turn the flywheel by hand. At the point you just feel the piston touch your finger and you are in the compression stroke (every 4th rotation), the spark should go off. If it goes off any other time, the timing could be out of phase, though with a single cylinder this is hard to do.
Moving on to petrol, it stands to reason the petrol should be clean and fresh. If you see a water bubble as the petrol floats on water, your fuel is contaminated. Water contained in petrol (a natural component) stored in a metal can left out in the cold can condense out of the petrol and goes to the bottom of the can. If this petrol is shaken up, the water doesn't re-enter the petrol but stays in suspension as tiny bubbles of water. These bubbles eventually fuse together and you get the condensate (water) separating from the petrol. Thus when you first crank the engine, it will propably start, until the first bubble of water kills the spark plug and the engine stops. It doen't run on water as water is uncombustible. If the engine splutters or back fires, the presence of water in the fuel is the first suspect. If it's a hot day and after several starts, the engine runs well after it warmed up, this means the engine is hot enough to evaporate the water and from this point will keep running, provided there are only a few droplets of water. if you leave the mower for a while and find it hard to start when the engine has cooled, this confirms the problem is water in the fuel.
These simple tests may be all that's needed. Beyond this, if the problem persists, it will require a technician to do more invasive tests. If you try these yourself you can easily void your warranty or severly damage the engine. Take it back to the dealer if you reach this point and demand your warranty rights.