You could probably learn how to play table tennis by watching other players, especially if those players are skilled and follow the rules. It is a fast-paced game that involves a lot of movement, and the little white ball is often whizzing through the air at impossible speeds. If you think that your eyes are quick enough to catch everything that is going on, then it's possible that you could pick up the rules and the techniques by observing.
The best way to learn, though, is by doing. If you invest in a beginning paddle and several of the 0 star ping-pong balls, then you can begin learning to play nearly immediately. It's a good idea to invest in some learning materials, such as books or training videos, or you can also find someone that has played before and ask for tips and rules.
As you are learning how to play table tennis, you should concentrate on several things. Your safety is foremost, so remember to warm up before you begin playing. It might sound silly at first, but after you complete your first game and feel the burn in your muscles, you will understand just how beneficial a warm up can be. You will be moving around a lot and swinging the same arm over and over again. Priming those muscles for movement and getting your heart rate up are important before beginning play.
There is also no way to try out the various techniques by just watching. If you are using the help of an instructional video, then you can watch the action slowly and on a smaller scale before attempting the swings and serves on your own. You won't necessarily learn how to play table tennis with just the videos, but they are a great way to start, and you can build your library as you learn.
Once you have mastered the beginning techniques, then you can learn from watching others. By learning the basics first, you become aware of what you watch for in other players. The best players have their own techniques and patterns, and you can pick up some of their ideas by observing them play. Just remember that you will need lots of practice to put your new ideas into play. Teaching others to play is also a great way to cement the things that you have already learned, and it will make you a more well rounded player.