This is the equation of a parabola, but it's lying on its side arms on either side of the x axis, which is the axis of symmetry, and the arms are on the positive side of x. The parabola's vertex is at the origin. The focus lies along the axis of symmetry and the directrix is a line x=-h. The rule about a parabola is that any point on the curve is equidistant from the directrix line and the focus point. Because of this rule when y=0, x=0 so the origin is midway between the directrix and focus, therefore the focus is at (h,0). Take any point P(x,y) on the curve. It's distance from the directrix is h+x; its distance from the focus is given by Pythagoras: sqrt((h-x)^2+y^2). But we know the equation of the parabola is x=y^2 so we can replace x and: h+2y^2=sqrt((h-2y^2)^2+y^2). Squaring both sides: (h+2y^2)^2=(h-2y^2)^2+y^2, y^2=(h+2y^2-h+2y^2)(h+2y^2+h-2y^2) (difference of two squares), y^2=8y^2h, h=1/8, because the y^2 cancel out. So the focus is at (1/8,0) and the directrix line is x=-1/8.
You've got the general picture of how the parabola looks, so you can mark the focus and directrix line, you know the vertex is at (0,0), and you can plot a few points to help you get the curve right. When y=1 and -1 x=2 and when y=2 and -2 x=8. That gives you 4 points: (2,1), (2,-1), (8,2), (8,-2). See how the x axis acts like a mirror reflecting each half of the curve.