If the company is doing well, and you can show how you have contributed to its success, your boss will likely be more open to discussing your request.
Have a plan in place.
Know which school you wish to attend; the major, or area of continuing education, you wish to pursue; the exact cost; and the length of time you estimate it will take to complete your degree.
Make an appointment with your boss.
With no human resources specialist to run interference, you'll have to speak with the boss directly. Do not try to catch him or her between meetings, or at the close of the day when everyone is rushing off. If you have a supervisor, and have a good relationship, you may want to enlist him or her to help in getting the meeting. Keep that person in the loop. Try not to give the impression that you are jumping the chain of command. If it is feasible, invite that individual to the meeting as well. It is likely you will have to go through a secretary or other administrative assistant. Inform that person that the nature of the meeting pertains to your professional development at the company.
Provide a deliverable.
A formal presentation with dimmed lights and a projector is probably not necessary. A document in memo format should be sufficient. Include the length of time you have worked at the company, your contributions whether in revenue-generating or cost-cutting measures, and your responsibilities. It would be helpful to include a brief rationale for how a raise (which, on a balance sheet, is an expenditure) would benefit the company. Attach copies of financial documents detailing tuition and fees, course outlines you have printed from the website, and contact information for the school.
Communicate your commitment to the company.
Make your enthusiasm for the company known, indicate that you wish to stay, and assure your boss that your education will not interfere with your duties.
Remind your boss of the bottom line.
Not only is tuition assistance a morale booster and an excellent retention tool, it is worthwhile from a financial perspective as well. The boss can expense it as a training cost. Present your case, and don't expect an immediate answer. Give your boss the opportunity to consider all the points. Close the meeting with the understanding that you will follow up within two weeks. If the answer is "no," don't be afraid to ask "why?" It may be something that you can fix. But don't hound your boss. Wait until your next performance review to bring it up again. Cut a deal. Try to make it part of your compensation package.