In this paper, we consider some methods for finding computable approximate solutions of Fredholm integral equations of the second kind. For integral operators with a smooth kernel and with a kernel of the type of Green’s function, various projection methods are investigated. Two types of projections, namely, orthogonal projections and interpolatory projections, are considered. The rates of convergence of approximate solutions are discussed and numerical results are given. For integral operators with a smooth kernel, Nyström method based on a convergent quadrature formula is discussed. Product integration technique for solution of a weakly singular integral equation is investigated.