The investigation of light-matter interactions is based on the description of the `photoelectric effect' in the early 20th century. The development of the first laser systems, especially of systems with high intensities and/or high photon energies, allowed to study previously unknown, non-linear effects like multiphoton or tunnel ionisation processes, which became subject of theoretical descriptions and experimental studies. Independently, the storage techniques for charged particles (electrons and ions) developed in parallel and different kind of devices, like Paul and Penning traps, had been invented in the 1950s and 1960s to study fundamental parameters of matter (for instance g-factor, mass etc.) with previously unknown accuracy. The HILITE experiment, presented within this thesis, is designed to combine and use for the first time the advantageous properties of target preparation a Penning trap can provide, like ensemble temperature, purity and localizability, in order to investigate laser-ion interactions at high intensities. Particular attention was paid to the compactness of the setup in order to be capable to transport the experiment to different laser facilities and perform experiments on site. In the frame of this thesis, the experimental setup was built and put into operation in terms of its dedicated ion source, ion selection, beam transport, deceleration and capture inside the Penning trap at the GSI Helmholtzzentrum für Schwerionenforschung GmbH. During commissioning, the storage and non-destructive detection of pure ion ensembles within the trap was demonstrated. The individual components have been characterised and their operation was checked. Additionally, a proposal was handed in for the first beamtime at an external laser facility (FLASH at DESY), which was granted and carried out. The interaction between the laser and low charged ions could be verified.