How to solve 2nd order inhomogeneous ODE with Green function?

Question

I'm studying Green function and get confused by some basic problems. For a 2nd order inhomogeneous ODE, we can solve it by constructing Green function.

$$y''+py'+qy=f(x)$$ where $p$ and $q$ are constants.

Quenstion:

1. How to construct Green function?
2. why does Green function $G(t,t')$ have different solution for $t<t'$ and $t>t'$?
3. How do boundary condition and initial value play the role for the construction of Green function?