The set you bought may have a problem, and so you should check each new set before using it. They are gorgeous. Not only do lights pose an electrical hazard, but the miniature bulbs are small enough to go in children's mouths and may pose a choking hazard. You should also unplug all of your indoor lights before going to bed or leaving the house. It's also a very good idea to have working fire extinguishers in your house, and especially near your tree.
Many people like to put up outdoor decorations, especially lights.
You should choose your outdoor lights as carefully as your indoor lights. Extension cords should also be UL-labelled for outdoor use. The outlets you plug the outdoor lights into are also important. If your outdoor outlets don't have GFCI's, have an electrician replace them before you use them. Do NOT try to test the GFCI by short-circuiting something, or indeed in any other way except by pushing the TEST button.