If you are a student, staff, or faculty member, you are eligible to use UTEP's ILL service.
However, some things-- like electronic copies of journal articles-- might be returned in as soon as 24 hours; materials that are difficult to find may take a little longer to arrive. Either way, there's no definite amount of time it takes for items to arrive. Just be sure to start your research early so that you'll have all your resources at the ready in a timely manner.
Also see the ILL Department's policies listed, in their own words.