The obvious danger is a large amount of super-hot oil.
The key tip is to make sure you put your fryer outside on a flat surface that is outside and your turkey is completely thawed.
Do not fry it indoors and do not use a fryer on a wooden deck, or in the garage.
Never leave the fryer unattended and make sure you keep kids and pets away from it.
If it does catch on fire, do not use water to put it out. Keep a fire extinguisher handy and call 911.