I don't know if I get your question, but here is something you can look into.
Fourier transform is basically converting a time domain function to frequency domain. That being said, Fourier transform basic formula gives you the amplitudes of various components of a given signal in frequency domain. Note the word amplitude. That's what Fourier transform provides you, amplitudes. These amplitudes are functions of, of course, frequency. By exponential Fourier transform formula, we get these amplitudes as complex quantities. That might be your $g(t) \iff G(f)$, where $g(t)$ gives the amplitudes of the signal vs. time, and $G(f)$ gives the amplitudes of the different components of the signal vs. their individual frequencies.
Now you are interested in PSD. That's power. So now you don't want amplitudes vs. frequency, you want power vs. frequency, right? Power is proportional to the square of amplitude. So how do you convert amplitude to power? You square the amplitudes.
But, amplitudes occur as complex quantities in exponential formula, remember? So if you multiply one complex quantity with its conjugate, you get the square of its amplitude. That's why you might use
Here, $G(-f)$ is the conjugate of the complex quantity $G(f)$. At $f = 0$, you of course get a real quantity. In that case, you have,
Hope that helps.