Heegaard Floer homology is a powerful invariant of three-dimensional manifolds whose computation is in general a challenging problem due to the role of holomorphic disks in its definition. In the case that the manifold is a link of a singularity, one can bypass holomorphic disks and compute Heegaard Floer homology using only combinatorial objects associated to the plumbing graph of the singularity. This talk will be a survey on these computation techniques and their applications to both low-dimensional topology and singularity theory.