Be careful of getting in too close to enemy infantry as that is the one time they can cause serious damage. Try and get them out with your own infantry if possible, if they survive long enough, it is about the only role in which they excel.
Try and learn
Various units have particular attack strengths: anti-tank guns do better against tanks, for instance, that standard artillery. Try and learn what is most effective against what and make the most of it, but do not be afraid to fire on a relatively ineffectual target if it is the only one offered.
Units
Units move, and then fire, and then they are spent for the turn. If you select a unit with targets in range it is often tempting just to blaze away, since they are more effective if stationary. But take a moment to ensure that there is no value in moving first, as you will not get the chance later.