PSD estimate using FFT - scaling and units
Have a look at this paper, section 9 goes over how to scale or normalize the FFT output. For the PSD you need to divide by the effective noise bandwidth (ENBW) which is

$$
ENBW = f_s\frac{S_2}{S_1^{2}}\\
S_1 = \sum_{j=0}^{N-1}w_j\\
S_2 = \sum_{j=0}^{N-1}w_j^{2}\\
where~w_j~is~the~jth~sample~of~the~window~function
$$