In this Tutorial, we consider plasma sources with applications to fusion devices and high energy accelerators. These ion sources typically produce negative ions from hydrogen-isotope gases, which are extracted through one or multiple apertures and accelerated to high kinetic energies. Next, they are either double stripped of two electrons to form positive ions used as precursors in accelerator devices or neutralized to produce a neutral beam injected in tokamak reactors. Contrary to the working conditions of most ion sources where volume production prevails, the mechanism of negative ion production by dissociative electron attachment on vibrationally excited molecules inside the plasma volume of fusion-type hydrogen-fueled high power discharges is mostly balanced by their destruction by detachment before being extracted rendering this means of producing negative ions rather inefficient. Surface production through the transfer of electrons from low work function metallic materials to the impacting atoms is the alternative solution to fulfill the requirements for the applications concerned. Negative ions are produced close to the aperture from which they are extracted. As a result, the analysis and understanding of the extraction mechanisms through experimental diagnostics is rather difficult due to the lack of accessibility and can only give a partial view. In addition, most of the experimental work is focused on the validation of requirements for the applications and not to the investigation of the fundamental processes that take place inside these types of sources. This Tutorial is focused on the description and understanding of the physical mechanisms behind the extraction and acceleration of negative ions from hydrogen plasma sources through modeling methods. We describe the numerical techniques of particle-based methods with a specific emphasis on particle-in-cell Monte Carlo collision algorithms. An analysis of the physical processes involved in driving the negative ions from the plasma source, across the apertures and inside the accelerator as reported in the literature, is presented in detail. This Tutorial concludes with additional and future works to be addressed in the coming years.