We provide a general procedure for computing the algebraic K-theory of finitely generated virtually free groups. The procedure describes these groups in terms of the algebraic K-theory of various finite subgroups and various Farrell Nil groups. We illustrate this process by carrying out the computation for several interesting classes of examples. The first two classes serve as a check on the method and show that our algorithm recovers results that already exist in the literature. The last two classes of examples yield new computations.