Vertical asymptotes occur when there is a value of x that does not exist. In your equation, all values of x give a solution (since x^2 is always positive, and there is a solution to all square roots of a positive number).
Horizontal asymptotes occur for when x gets infinitely large or small. this is slightly more tricky to deal with, but plugging in some large x and negative x values into the equation will give you a feel for what's going on.
The other things to consider are where the graph crosses the x and y axis. Eg, what is the value of y when x=0, and vice versa. (This is quite easy for this equation.)
Finally, you will need to consider any stationary points. These are found by differentiating the equation and identifying where f'(x)=0.
The final comment is that it's useful to put in some real values of x to make sure that the graphs is correct as a check.