The authors generalize results from the commutative geometry to the noncommutative case. They extend the coherent state approach to the fuzzy sphere by developing the noncommutative version of spinor calculus. Section 2 contains the reformulation of the standard spinor formalism of \(S^2\) to the more algebraic language. The generalization to the noncommutative case is described in Section 3, and a complete set of eigenstates of the Dirac operator on the fuzzy sphere is found. The results are briefly discussed in Section 4.