It is ok to tip your Ariens push lawn mower on its side, but only on the side where the oil is added. Tipping the mower on the other side will allow oil to leak into the cylinder.
To fix this problem, set the mower back upright and let it sit, this will let the oil drain back into the crankcase. Remove the spark plug and clean it off by spraying carb cleaner on it or replace it because it will most likely be coated in oil. Also, check the air filter to see if it has oil on it, if it does then replace it. Check the oil level and fill it up as needed. Once you try starting the push mower back up there will most likely be white smoke that is just the oil burning up. It should be good to go after that.
You can find the model and serial numbers located on your Ariens push or self-propelled lawnmower at the rear of the mower, to the right or top of the discharge area. The model number will be 6 digits starting with a "9".
NOTE: if you need a part for the small engine in your Ariens push or self-propelled lawnmower, there will be a separate model/serial number for the engine. Here are the small engines that are available in your Ariens push or self-propelled mower. Visit the page of the engine you have to find out where the model/serial number is located for your small engine model: