Algebraic modular forms are certain objects in the theory of automorphic forms which are particularly well-suited for computations. The space of modular forms comes equipped with an action of the so-called Hecke algebra and one of the main problems is to determine this action explicitly. In this talk I want to introduce the basic concepts of the theory, explain the classic algorithmic approach to the arising problems, and in the end present a somewhat novel method to determine the action of certain Hecke operators. This new method employs the adjacency relation in the Bruhat-Tits building to compute certain operators simultaneously and yields a significant speed-up compared to the usual methods.