They can occur any time of the year, but are most common in the spring and early summer around here. Historically may is the month for the most frequent and most severe, with April and June close seconds. When the storm conditions are right, multiple tornados can drop down, it is common for several to form in the area at the same time. Keeps the TV weather folks real busy tracking them all to keep people informed. There will often be 10 or more within a 200 mile radius in really active storms.
I don't know the technicalities, but it seems most tornados are caused when warm moist air collides with a cold front, and with big active thunderstorms. The rise and fall of the warm/cold air causes what they call 'wall clouds', then the circulation forms and the tornados spin down out of the clouds and travel along the surface of the land. Small ones may be only 100' wide with winds around 100mph, but the massive F4 tornadoes are a mile or Two across with 200-250 mph winds----those are the killers and just leave bare house foundations behind them.