Start with a diagram. Show the rod, the coordinate axes, and the point
P. Make your diagram BIG.
Step I: Model the system (the rod) as a collection of differential elements. Draw a typical element on your diagram. Each element should correspond to a differential change in one coordinate.
See diagram above
Step II. Identify a typical element and describe it using your coordinates.
The element extends from x to x+dx and has charge dq = l dx
Step III. Express the contribution of your element to the desired sum. (i.e. find the electric field dE produced by this element. Give both its magnitude and its direction. With vectors, it is often easier to calculate each component separately.
As we can see from the diagram, the electric field is in the x-direction,
and from Coulomb's law
Step IV. Find the limits of the integral.
The limits are x = -a to x = a
Step V: Integrate!