A common theorem is that every projective modules over a PID are free and we know that every projective modules over commutative local rings are free too. Also every finitely generated projective module over a polynomial ring $K[x_1,\ldots, x_n ]$ over a field $K$ is free (Serre Conjecture) and in 1976 proved by Quillen and Suslin. I want to know for $n=2$ how it works.
Any comments and guidances are very welcome.