How to calculate vibrational spectra of organic molecules?
The usual approach is:


Find the equilibrium geometry (within the Born-Oppenheimer app.).
Expand the energy in Taylor series till second order term. The first order will be 0 because of the minimum energy condition.
Include this expression in the Hamiltonian.
Generate a coordinate transformation to get normal coordinates.
Relate second order derivative of the potential energy with the force constant of Hook law (Using second order term we can identify it with a harmonic oscillator). Then get the harmonic frequencies.
The software employed should give also the intensity for each frequency.
Plot intensity vs. frequency/energy/wave length. You'll get only "points". To transform them to a continuous function you can use a Lorentzian like function.


Details can be found in most computational quantum chemistry books.