Many incoming PhD students are supported during the first year of studies by money from the University. This support includes a stipend and tuition waiver. At the beginning of each year, you will have to pay some money for fees, health insurance, and possibly parking, but this amounts to a few hundred dollars. If you have your own health insurance, you can have this portion of your fees waived.
In return for support, the department requires you to perform some service to the department. PhD students are required to serve four semesters as teaching assistants or ``labbies''. Responsibilities include grading, designing homeworks, projects, etc. You will rarely be asked to lecture. Grading is an important responsibility and should not be taken lightly.
The stipend covers the academic year only, and does not continue into the summer. After your second semester, you must obtain support from a research grant. This means you will probably have to do some research in addition to labbying. However, this will give you exposure to research and will hopefully help you decide what research area interests you. There is no guarantee that after your first year you will find a professor willing and/or able to support you. If you are unable to find a professor willing to support you during your second year, the department may make some effort to find money from other sources. If by the beginning of your third year you still have not found a professor willing to support you, then support becomes a serious issue, and you should consult with members of the graduate committee. We cannot guarantee that you will always be supported throughout your graduate career. It is your responsibility to secure the agreement of a faculty member to advise and support you during the research phase of your graduate studies. You should begin planning for this step as soon after your arrival at Rice as possible.
Master of Computer Science (MCS) students are generally not supported. There are a few special fellowships for these students, but these are few and far between. The Financial Aid Office may be able to provide you with a list of external sources of funding.