Estimating the Impulse Response of the Room Using Sweep Signal Microphone Recorded Signal (Input & Output of a Convolution)
this is the two-channel FFT method of spectrum analyzer:

$$ y[n] = h[n] \ \circledast \ x[n] $$

just make sure that the length of the FFT $N$ is at least as large as the length of sound $x[n]$ plus the expected length of the impulse response $h[n]$.  the length of sound $y[n]$ is also as long as the FFT.  you can round $N$ up to the nearest power of two.  just zero-pad everything to that length and then 

$$H[k] = \frac{Y[k]}{X[k]} $$ 

is functionally true.

you might sometimes have to worry about division by zero, but if your driving signal $x[n]$ is sufficiently broad-banded (which a linear sweep or a maximum-length sequence is), then you don't have to worry too much about division by zero.

if you know $H[k]$, then you know $h[n]$.