There are a few simple safety rules that you must observe when burning incense or candles, or using an oil-burner...
1) Use a proper holder. All types of incense andcandles need to be held firmly in a proper holder so they won't fall over. The holder needs to be stable too, so it won't fall, or be knocked over.
2) Put them on a heat resistant surface. Be especially careful with metal incense holders and night lights / tea lights, which can get hot enough to melt plastic!
3) Don't put incense or candles too near curtains or other fabrics. And keep candles out of draughts. Keep burning incense or candles out of the reach of children or pets.
4) If there's any chance you could forget it's there, and lean across a burning candle or incense, put it somewhere else. You don't want to set fire to your clothes or your hair.
5) Never leave burning incense or a candle unattended. Extinguish incense and candles before you leave a room. Never go to sleep with incense or a candle still burning. And never leave a burning candle, incense or oil burner in a bedroom - especially a child's bedroom!
6) Never allow an oil-burner to boil dry. Depending on the type of burner, it could break - or even catch fire in some cases!
Finally, please don't forget to allow adequate ventilation when you're burning incense... you want to enjoy the fragrance, not end up being smoked like a kipper or choked half to death!