The arrow at the beginning of the spline adjusts the 
number of items in the array.
You can also input a number in the options panel.
The arrow at the end of the spline allows you to add 
more spline points by clicking or click-drag.

Click-drag on the sphere-shaped widgets to move
the spline points in the middle of the array, if desired.

Note that by using Grid Mode and toggling on/off
appropriate axis, you can keep things nice and straight.

There is another mode of editing the spline, to enter it
right-click on one of the spherical spline move widgets.
 

A new spline edit toolbar pops up.

You may now adjust move points by click-drag
on the yellow handles, or the point in the middle.
Note that by holding Control or Shift keys you
can adjust each handle independantly.

You can add or delete points, open or close splines,
and toggle between adjusting all or just one point
at a time.