Obtain an appointment with the committee. If it's going to be a face-to-face one, an appointment will likely be necessary. Make the necessary arrangements to have your time to speak to the committee.
Educate yourself on university bylaws if necessary. If the reason for your previous departure from college has to do with an indiscretion on your part, take some time to read up on the university policy that you violated and learn about any loopholes that could make it easier for you to get around the trouble you have created. If you can find an exception to the rule that left you out of college, you may be able to strengthen your case.
Plan what you intend to say. Careful planning can ensure that you make your case as effectively as possible. While you could speak off-the-cuff at your committee meeting, doing so jeopardizes your chances of re-establishing your relationship with the university as you likely won't be able to make your case as eloquently. As you set about making your plan, write the reason why you previously broke ties with the university on a sheet of paper, then list supports as to why they should readmit you below it.
Practice your presentation. Ask a friend to act as the one-man readmissions committee and listen to your presentation. After he listens, ask him to critique the presentation so you can perfect your presentation before the meeting time.
Be humble. When asking a readmissions committee for mercy, you don't want to appear arrogant. Prepare yourself to adopt a humble demeanor to increase your chances of gaining readmission to the university in question. Appearing likable can play a major part in getting you into the committee members' good graces.