The best overview over current techniques in quantum chemistry is "Molecular Electronic-Structure Theory" by Helgaker, Jörgensen and Olsen.
About "LCAO": The term "LCAO" should not be understood too literally. "Atomic orbitals" in the modern terminology are simply any kind of local basis functions placed on atoms. Some of the functions in a basis set are actually built to resemble atomic orbitals (i.e., solutions of the Hartree-Fock equations for atoms), but most are not.
A "molecular orbital" is then a one-particle function satisfying some kind of mean-field one-particle Schrödinger equation (usually the Hartree-Fock equation, or the Kohn-Sham equation). Molecular orbitals are typically expanded as linear combination of non-orthogonal local basis functions like this:
\phi_r(\vec x) = \sum_{\mu} C^\mu_r \phi_\mu(\vec x),
where r indexes the molecular orbitals (occupied or virtual) and \mu the basis functions (which are often called ``atomic orbitals''), and C^\mu_r is the orbital coefficient matrix.
This matrix is what is actually determined in a calculation of orbitals (like Hartree-Fock or Kohn-Sham).
If doing wave function methods, these orbitals are then used as input for a so called ``correlation calculation'' (e.g., some coupled cluster method), in which accurate wave functions are determined based on the Hartree-Fock wave function as a initial approximation to the electronic structure of the system.
The orbitals themselves usually do not have any strict physical interpretation. The most one can hope to get from them are (unimpressive) ionization energies via Koopman's theorem.
