Here is the simplest version for plotting a vector field

VectorPlot[{-y, x },{x,-1,1},{y,-1,1}, VectorScale -> Automatic]

Here is a fancier version.

xMin = -1;  (* Change the screen limits here *)
xMax = 1;
yMin = -1;
yMax = 1;
F[x_, y_ ] = {-y, x};  (* Change the vector valued function here *)
Print["The vector field of F(x, y) = ", F[x,y]]
VectorPlot[F[x,y], {x, xMin, xMax}, {y, yMin, yMax}, FrameLabel ->{x,y},VectorScale -> Automatic]