Answer
Shift 2 units to the left, then one unit down (see graph)
Work Step by Step
We are given the functions:
$f(x)=x^2$
$g(x)=f(x+2)-1$
In order to graph $g(x)$ we first shift the graph of $f(x)$ by 2 units to the left to get $f(x+2)$, then shift the graph of $f(x+2)$ one unit down to get $f(x+2)-1$: