In our recent Communication (J. Chem. Phys. 2016, 144, 011101), we proposed Wick's theorem for nonorthogonal determinants and applied it to spin-extended configuration interaction with singles and doubles (ECISD) based on spin-projected unrestricted Hartree-Fock (SUHF), given that SUHF is a special case of nonorthogonal CI. It was shown that ECISD is accurate for bond-dissociation processes of several representative molecules. In the present work, we give a detailed derivation of ECISD and report an efficient implementation with two physically motivated preconditioning schemes in the generalized Davidson diagonalization for ECISD, whose Hamiltonian and overlap are not diagonal dominant due to SUHF's nonorthogonal character. In the first approach, we exploit the properties of corresponding pair orbitals and spin-projection operator and rotate the spin-projected CI basis so that the Hamiltonian is approximately diagonal. The second scheme is based on the normal ordered Hamiltonian, which suggests neglecting the expensive two-particle terms in the preconditioning. To enable frozen-core approximations in ECISD, core orbitals were introduced in SUHF. We also show the validity of our method with various numerical examples for static correlations, apart from the left-right correlation in bond-dissociation processes: the ground state energies of the Be isoelectronic series, excitation energies of representative small molecules, and spectroscopic constants of the strongly correlated BN singlet state. Several aspects of ECISD were studied.