  We develop a method for computing form factors of local operators in the
framework of Sklyanin's separation of variables (SOV) approach to quantum
integrable systems. For that purpose, we consider the sine-Gordon model on a
finite lattice and in finite dimensional cyclic representations as our main
example. We first build our two central tools for computing matrix elements of
local operators, namely, a generic determinant formula for the scalar products
of states in the SOV framework and the reconstruction of local fields in terms
of the separate variables. The general form factors are then obtained as sums
of determinants of finite dimensional matrices, their matrix elements being
given as weighted sums running over the separate variables and involving the
Baxter Q-operator eigenvalues.
