Step 1 :The function \(y=2^{x-3}-1\) is a transformation of the function \(y=2^{x}\).
Step 2 :The '-3' inside the exponent shifts the graph 3 units to the right.
Step 3 :The '-1' outside the exponent shifts the graph 1 unit down.
Step 4 :\(\boxed{\text{The graph of } y=2^{x-3}-1 \text{ is the graph of } y=2^{x} \text{ shifted 3 units to the right and 1 unit down.}}\)