In this thesis I describe the experimental setup for laser cooling and trapping of cesium atoms which was developed in the Cold Atoms Laboratory at the Jožef Stefan Institute. I put a special focus on the device which slows down the atomic beam - the Zeeman slower. Its development is described in detail as well as the necessary theoretical background. The suitability of the constructed Zeeman slower is evaluated with the Monte Carlo simulation of the beam slowing process. The description is rounded up with the measurements that were made during the early tests of our laser cooling apparatus. Our Zeeman slower produces a beam of slow atoms which travels towards the magneto-optical trap, where the atoms are cooled down to the temperature around 1 mK. Long-term goal is to achieve the temperatures around few nK, but the entire path towards that goal is not presented in this work. Instead, the description of the experiment is limited only to the components that were developed simultaneously with the Zeeman slower and which are closely related to it.