Nothing about Olmec society is precisely known, but archaeologists can make educated guesses, and some have. They believe the Olmec were a highly developed civilization with a calendar, system of writing, bureaucracy, organized religion and many techniques for creating beautiful and valuable objects. For this last claim, the evidence is the objects that are left to us; however, we cannot be certain what the purpose of these objects was. It is widely supposed that they filled a religious role, being part of ceremonies or decorations for temples, and not being privately owned.
In any case, to produce the works of art we have found, there must have been a rich and supportive tradition of Olmec artists, perhaps associated with a priest caste in some sense. Stone artworks are neither easy to make, transport nor obtain raw materials for, and with the tools available at the time, the level of definition and refinement of form apparent in some artifacts must have required intense devotion and focus.
Olmec artifacts were most likely made with stone tools, because there is a complete absence of evidence for the use of metal tools in Olmec society or its contemporary neighbors. Individual pieces of art show evidence of drilling and sawing, but it is not known if drills and saws were the only tools the Olmec used. Certainly, it is hard to imagine that saws and drills could achieve the subtle detail and precisely controlled planar angles of an Olmec face alone.
Much of Olmec art has an incredibly polished, glossy finish to it; archaeologists don't know how the Olmecs achieved this technique. They note that it is a higher level of polish than they can satisfactorily explain, and hope to uncover evidence in the future that might shed light on whether the Olmecs used other tools or special techniques. Treasure hunters removing Olmec artifacts from their original contexts -- seeing these ancient artifacts only as a source of wealth, not knowledge -- complicates this investigation, as it does other archaeological endeavors.