We report an experimental apparatus and technique which simultaneously traps ions and cold atoms with spatial overlap. Such an apparatus is motivated by the study of ion-atom processes at temperatures ranging from hot to ultra-cold. This area is a largely unexplored domain of physics with cold trapped atoms. In this article we discuss the general design considerations for combining these two traps and present our experimental setup. The ion trap and atom traps are characterized independently of each other. The simultaneous operation of both is then described and experimental signatures of the effect of the ions and cold-atoms on each other are presented. In conclusion the use of such an instrument for several problems in physics and chemistry is briefly discussed.