Answer
asymptotes: $y=\pm x$
foci: $(\pm2,0)$

Work Step by Step
Step 1. Rewriting the equation as $\frac{x^2}{2}-\frac{y^2}{2}=1$, we have $a=b=\sqrt 2, c=\sqrt {a^2+b^2}=2$ centered at $(0,0)$ with a horizontal transverse axis.
Step 2. We can find the vertices as $(\pm\sqrt 2,0)$ and asymptotes as $y=\frac{b}{a}x=\pm x$
Step 3. We can graph the equation as shown in the figure with foci at $(\pm2,0)$