Choosing a particular sport is your first goal. If you're planning on starting a league with a group of friends, take a poll to determine what everyone would most enjoy. It's your league, however, so if you're passionate about a particular sport, feel free to run (or skate or jump) with it!
Next, you need to decide the scope of your organization. Are you envisioning four small teams that rotate weekend games among each other? Or would you prefer dozens of groups, complete with matching jerseys and an end-of-season tournament? Obviously, the larger the scale, the more effort it's going to require on your end, so don't act on those grand ideas you've been kicking around until you've done some research.
Once you've determined the size of your program, you'll need to locate facilities for practices and games. The Web site of your county's parks and recreation department is a great place to find this kind of information (or to get the phone number of someone who will be able to help you). You'll need to determine the fees for renting park space, including the cost for lights, venders and anything else a burgeoning sports league might need. Once you calculate the total potential cost of your season (which will vary significantly between cities, counties and states), split the amount between your teams, which can raise the money through player dues.
Of course, you won't have much of a league without players and coaches. Advertise via word-of-mouth, social networking sites, free newspaper announcements or fliers posted (with permission) around town. Many adult leagues simply appoint a team captain, but anything youth-centered will require a volunteer coach, often a parent or teacher.
If you decide that starting your own league requires more effort than you anticipated, try looking into existing local programs. Joining a team is significantly less work than founding an entire intramural program, and your county's parks and recreation department and the local YMCA are both excellent resources for amateur athletes looking to join or start a team. Rates vary based on the sport, length of season and location, but are generally nominal and usually cost somewhere around $100 or less.