The first column of the matrix corresponding to the the transformation T with respect to the bases in V and W is the coordinates of T(v1) with respect to the basis in W.

In other words, calculate T(v1), which will be a vector i W. Write this in terms of the basis in W, so T(v1) = c_{11}w1+c_{21}w2 + ... + c_{m1}wm, where the c_{i1} are scalars. Then the first column of the matrix consists of exactly these scalars.