Instructions
Left-click a unit to select it, or left-click and drag to draw a box and select multiple units. If the units are capable of attacking, an "Attack" cross hair will appear alongside the other command buttons on the bottom right.
Right-click an enemy unit or building to give attack orders. If the target is in range, your units will immediately attack; otherwise, they will move into firing range first.
Give the "attack-move" order by left-clicking the "Attack" button on the bottom right or pressing the "A" key, then left-clicking unoccupied ground. Your units will move to the specified location, stopping to attack and destroy any enemy units they see on the way -- units that would be ignored with a normal Move command.
Attack your own units or buildings -- to clear ground, reduce supply use or deny enemy access to abandoned buildings -- using the "Attack" button or "A" key, since right-clicking will only issue a Move command.