There are currently only three recognised modes of warfare in the modern world; maneuver, attrition and guerrilla. This article will mostly focus on the first of this triad, but the other two will be mentioned. Guerrilla warfare is generally the province of privateers, they operate behind the lines attacking enemy lines of communications. Attrition is the principle tactical mode of engagement, since all space combat is basically naval, however maneuver is important as well.
The problems facing fleets
At the tactical level we have a problem. Missiles need to be stacked up against targets to be effective, this is referred to as mass. So ideally you'd concentrate all fire against a single target. To defend against mass attacks you want to have a literal "forest" of point defence lasers. The ideal situation is thus for all ships to be stacked in a single hex. However, there's another problem, that of finding the enemy and bringing it to battle. By the book, all contacts are initiated at about 30 hexes (1 light minute), which means that the sensor area cover is far too small for operations in a star system, you need to disperse platforms to look for the enemy.
The Battlegroup system, similar to Napoleons's Corps de Armee system. The WW2 CVBG system is less like our 2300 BG, due to different craft and capabilities. We don't have a real aircraft equivalent, and weapons are comparitively far less lethal.
The 2300AD Battlegroup is ideally composed of a number of "Ships of the Line", Battleships, Cruiser and Destroyers, stacked together. The Battlegroups should be spaced apart by about 30-60 hexes. At this kind of distance their sensor bubbles overlap, and nothing can get between them, but they are close enough that they can react to reinforce each other. At 60 hexes apart, in 10 turns the neighbouring battlegroups can have converged.
In front of the battlegroups we should place a screen of frigates, fighters and sensor drones to act as forward scouts. Their job is to locate and fix the enemy, while the BGs behind them maneuver to attack. The fact that our scouts are actually slower than our battleline shouldn't be a worry, the battlegroups are coming up as quickly as they can, and if the frigates are pushed forwards a whole light minute, the battlegroup will be up with them in just five turns, for Kafers this is a similar amount of time a single round of a missile exchange would take. Frigates thus only need to be able to survive the one missile exchange.
Example: Graham's force at Beowulf
The QAS system has a closer cut off, but the planet is deeper in the system than Sol. The QAS FTL shelf is 1.94 AU out (458 hexes in radius), the planet is 348 hexes from the shelf at it's nearest point. Triumphant Destiny divided its fleet into 2 wings, one coming from the point of closest approach, and driving straight in at 4 hexes/ turn. They will have taken 87 turns to reach Beowulf orbit from closest approach. The second wing came in with the sun between Beowulf and them, intending to bypass the fleet and strike Beowulf directly. Graham was wise to the possibilty, and a number of his frigates were stationed at the periphery of the system. To provide complete coverage of the perimeter would take 24 ships, even thinking 2 dimensionally. If you allow for the third (which the game doesn't) it's near impossible. He simply doesn't have the ships, but technology allows for Sentinels to do the job of the outer ring. With some frigates in a second, inner, line retiring while maintaining contact with the enemy. TD's gambit failed here, because it had never encountered such organised resistance.
The main Battlegroups will be arrayed around the main flagship vessels. The American USS Columbia was the flag of the reserve battlegroup, while the Flagships HMS Victory, HMS Britannia, HMS Prince of Wales and IFS DeGaulle will be the C4I ships for the 4 Battlegroups in the line. The final major unit will be the Carrier Group, with the Fighter Carriers Joffre and Ark Royal behind the main line, in a supporting position.
Given the well co-ordinate two front attack, we can expect that Graham will be forced to fight on two fronts around Beowulf (rather than striking out at a single incoming group). We can expect that Graham but 2 BG on each front, with 2 BG (Columbia and Carrier) in between the two as a reserve. There are 14 Cruisers and 20 Destroyers filling out these lines, including those of 2 nations without a Flagship, these will be parcelled out to mostly the main BGs, with perhaps the American vessels out of the line with Columbia. There are also 27 frigates insystem, some of which are detached to the outer system, but others will be acting independently around the line. Columbia's American commander noticed that a Kafer BB was holding back and moved out of her reserve position to attack it. Had it not been TD's flag, she'd have been hanged for it it, but it was and she distracted the Kafer flag in a 2 hour (6 turn) engagement, ended by the arrival of the fighter strike which was intended to take her out. After their C4I broke down the Kafers retreated, while a pursuit developed. The Columbia was probably meant to be a Corps de Chasse (an exploitation unit, designated to pursue a broken enemy).
The Kafers lost 8 starships in the battle, and another 8 were destroyed during the pursuit. Eight escaped further up arm. Richelieu's force (which was 4 Battlegroups with 1 CV, 3 BB, 10 CG, 8 DD, 18 FF) (Once of the CG is actually a CGL) failed to move into position as a blocking force in time, showing the problems of interstellar communications.
Example: The Aurore force
This force starts with 2 BB, 4 CG, 2 DD and 8 FF, but is quickly reduced to 1 BB, 4 CG, 2 DD and 6 FF in the opening battles. This fleet is organised into 2 divisions, fast and slow. The fast division is led by Borodin on the Bismarck, with the 4 Cruisers and 2 Destroyers, while the slow division is the frigates (commanded by Lutke?). After reinforcement by 2 BB, 2 DD and 3 FF this structure seems to be expanded, with 3 seperate groupings, 2 Battlegroups based on the Napoleon and Guderian forming the heavy battle force, while the light force is stiffened by the Bismarck (assumidly Lutke getting his flag back).
Scale: I've maintained hex sizes, but had to rescale the turn length to fit.
A good article on the Corps throughout history: http://www.wargamer.com/articles/maneuver.asp