The first thing you want to do to start your own club is to gauge the interest of others. If you can only get three people together, it's not much of a club. Drum up some interest among people you know and have them spread the word via the Internet and social media.
Next, you need to decide on what kind of club you want. It can range from an informal group that has a regular place to play to a real league with a management hierarchy to actually opening up your own business, kind of like a pool hall for table tennis.
If you want something informal and need a great place to play, then put the word out for spaces. Having a group of members in place helps this process out. If you want a more organized league, you'll not only need a place to play, but you'll also need to come up with the structure of the league -- teams, number of matches, tournaments, etc. You'll also want to structure the league hierarchy by electing a president, vice president and a secretary/treasurer to handle things like rules, dues and meetings. It helps to join the USA Table Tennis (USATT) organization, the leading pingpong body in the United States. It can help you with regulations and official club bylaws, as well as getting the word out about your club. If you have the will and you follow these steps, before you know it you'll be swamped with eager players, paddle in hand.