We have recently demonstrated the creation of regular strings of neutral caesium atoms in a standing wave optical dipole trap using optical tweezers [Miroshnychenko Y et al 2006 Nature (London) 442 151]. The rearrangement is realized atom-by-atom, extracting an atom and re-inserting it at the desired position with submicrometer resolution. We describe our experimental setup in detail and present systematic measurements as well as simple analytical models for the resolution of the extraction process, for the precision of the insertion, and for heating processes. We compare two different methods of insertion, one of which permits the placement of two atoms into one optical micropotential. The theoretical models largely explain our experimental results and allow us to identify the main limiting factors for the precision and efficiency of the manipulations. Strategies for future improvements are discussed.