Network function virtualization has received attention from both academia and industry as an important shift in the deployment of telecommunication networks and services. It is being proposed as a path towards cost efficiency, reduced time-to-markets, and enhanced innovativeness in telecommunication service provisioning. However, efficiently running virtualized services is not trivial as, among other initialization steps, it requires first mapping virtual networks onto physical networks, and thereafter mapping and scheduling virtual functions onto the virtual networks. This paper formulates the online virtual function mapping and scheduling problem and proposes a set of algorithms for solving it. Our main objective is to propose simple algorithms that may be used as a basis for future work in this area. To this end, we propose three greedy algorithms and a tabu search-based heuristic. We carry out evaluations of these algorithms considering parameters such as successful service mappings, total service processing times, revenue, cost etc, under varying network conditions. Simulations show that the tabu search-based algorithm performs only slightly better than the best greedy algorithm.