The main key in the approach battle is when during the turn you reach medium range. For example, disruptor-using races often want to soften up their enemy with a range-15 shot before closing to overload range. They want to end the turn just inside of 15 hexes, while their enemies probably want them either outside or well inside that range.
Maneuvering at this range is mostly about controlling the range. In fleet battles, though, which shield is being hit becomes important as it can be eroded before closing.
Plasma-using races may use a version of the sabre-dance by using the plasma bolt (i.e. direct-fire) at range 10 -- known as the Glory Zone. Plasma bolts are particularly ineffective beyond range 10. This is a more difficult maneuver since the plasma ship needs to reach range 10 but avoid range 8 (where a direct-fire opponent can use overloads).
This is a threatening range: close enough to crack shields, with the chance of doing internals on a fresh shield. However, it can be disastrous to fire at this range if the opponent then takes the opportunity to close to point-blank and take a real killing shot.
One vital tactic at this range is bluffing. As you get into this range, the opponent may put his power into shields and weapons rather than movement, expecting to close for the better shot. At range 8, you fire your weapons and move out of range 8 the next impulse, denying him an equal shot in return. However, this is extremely risky. If he can close with you before the end of the turn, you may take more than you gave and be in a poor position for later.
An important tactic here is considering early fire. If you hold all your weapons for a closer range shot, then some weapons may be destroyed before they can fire and you might not be able to get into that close range. Thus, some players will fire 1 torpedo and 2 phasers early -- thus weapon hits will be spent on already-fired weapons.
On the other hand, the opponent may be able to turn so that your `early' fire is on a different shield than your close-in strike. This can cost you internals.
The next turn then becomes known as `knife-fighting', when the ships sit still or move very slowly. At this point, TAC maneuvers are better for turning than normal movement. Usually a lot of power goes into weapons plus tractors, negative tractor energy, and/or shield reinforcement.