If we are using Newton's method (or gradient descent), how do we find a maximum instead of a minimum?

Yes, that's exactly what you do. You can think of this sign change as causing you to perform gradient ascent instead of gradient descent (in the case of using a gradient method). Alternatively, you can think of flipping the sign in a gradient method as performing gradient descent in $-f$. By finding a minimum of $-f$ you find a maximum of $f$.
Similar reasoning holds for Newton's method (and various other methods as well).