The task of counting the number of spanning trees in a graph is generally challenging and cannot be solved using simple elementary counting techniques. Although it is difficult to count all spanning trees in the general case due to the size of the solution space, there are graphs for which the number of spanning trees is well known. This work aims to describe and implement the formula and algorithms for some of the basic methods of counting spanning trees. First, Kirchhoff’s formula was implemented, which is the most efficient way to obtain the number of spanning trees, but it only gives their number without finding the actual trees. Therefore, we resorted to other algorithms and focused on some of the well-established methods for counting trees. We developed an algorithm that uses the test and select method, which has a high time complexity and is therefore inefficient. Consequently, we implemented Minty’s algorithm, whose complexity grows linearly with the number of spanning trees. Although Minty’s algorithm is much faster than the previous one, it should be noted that the solution space grows rapidly with the number of edges and vertices, and therefore, the execution time can be long for large graphs.