We consider how to effectively compute the combinatorial multigraded link Floer homology ofknots and links, then implement it. The goal being to compute the invariant for knots and links for which it is unknown, and further develop the algorithm for its production. We review a traditional description of knot Floer homology and motivate it. Then we move to the combinatorial description of the theory known as grid homology. From there we consider and implement an algorithm leveraging some changes in perspective and tools afforded by modern computing. Finally, included at the end is a compilation of some standard properties of the invariant for examples computed using the resulting program. From the resulting directed graphs we extract the Poincar ́e polynomial along with some properties of the invariant for each sample knot.
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