Look at your field allowance. If you only have 1 field, typically you can only have about 8 teams play when you decide "How do I organize a softball tournament". You must know this number before you start accepting teams.
Determine a prize. It could be a cash prize or something simple like T-shirts. For the most part, people don't care. They just like to play the game and have a good time with friends. You must consider the prize, however, when you decide "How do I organize a softball tournament".
Call your local "Parks and Recreations" department and actually ask, How do I organize a softball tournament. Give them your ideas. This is a great way to come up with a date that works best. Also, sometimes the department will advertise for you and call existing teams to join.
Post fliers around town. If you have a free advertisement newspaper, place an ad about a month before the date. Give everyone a couple of weeks for the deadline. Once you get over the initial amount of work required when you find out, "How do I organize a softball tournament", everything seems to fall into place.
Contact local food vendors and ask them if they'd like to participate in your event. They could even make a bit of money over the weekend. You always need food when you ask yourself, How do I organize a softball tournament".