Here is a picture to add to Robert's good answer demonstrating the "re-use" of operations, in this case for an 8 point DFT. The "Twiddle Factors" are represented in the diagram using the notation $W_N^{nk}$ which is equal to $e^{j2\pi \frac{nk}{N}}$
Note the path shown and the equation underneath shows the result for the frequency bin X(1), as given by Robert's equation copied below:
$$ X[k] = \sum\limits_{n=0}^{N-1} x[n] \, e^{j 2 \pi \frac{nk}{N}} $$
Dashed lines are no different than solid lines just to make clear where the summation joins are.
