There are a few things to keep in mind when using an electric space heater. They are perfectly safe to use as long as you remember the following things outlined here.
The first tip would be that if you plan to leave the room you are heating for an extended length of time, you should be sure to turn off the heater just to be cautious.
Second, while many heaters are safe to use on carpeting, you should be sure that the carpeting isn't too long. If its long enough to each into a heater's air holes, it could be disastrous. To be safe, it'd be best to place the heater on top of something to distance itself from any long carpetting.
Lastly, as with all electric devices, you should be careful about having water or other fluids near it. If water spills into it, not only could it ruin the heater, but it could cause electrical damage.
Remember, heaters can be as safe as any electronic device in your home, but you have to be sure to remember that safety comes first! Happy heating!