Which best describes the transformation from the graph of $f(x)=x^{2}$ to the graph of $f(x)=(x-3)^{2}-1$ ? left 3 units, down 1 unit left 3 units, up 1 unit right 3 units, down 1 unit right 3 units, up 1 unit

Step 1 ：The transformation of a function can be understood by looking at the changes in the function's equation. In this case, the function \(f(x)=x^{2}\) is transformed to \(f(x)=(x-3)^{2}-1\).

Step 2 ：The \((x-3)\) in the equation indicates a shift to the right by 3 units (since it's subtracting 3 from x), and the \(-1\) at the end of the equation indicates a shift downwards by 1 unit (since it's subtracting 1 from the whole function).

Step 3 ：Therefore, the transformation from the graph of \(f(x)=x^{2}\) to the graph of \(f(x)=(x-3)^{2}-1\) is right 3 units, down 1 unit.

Step 4 ：Final Answer: \(\boxed{\text{right 3 units, down 1 unit}}\)