Mentoring undergraduate students in research is both rewarding and challenging. In this paper we present how we established a summer Research Experience for Undergraduates (REU) program in the mathematical sciences at Michigan State University. A goal of our REU is to include students who are at an early stage of their study of mathematics. We share our experiences in recruiting students, designing research projects, and mentoring our participants. We discuss the challenges we faced and the solutions we found while working with a diverse group of undergraduate students from across the nation.