Like most games, assaults (close combat) is particularly brutal in BA. Essentially once a unit is given a Run order and can move into contact with an enemy infantry or artillery unit it can then execute an assault.If it started the assault greater than 6 inches from the target unit, that target gets to conduct a round of defensive fire as per the shooting rules above. All pins are ignored, and all survivors of the assaulters then get to attack.In fact as soon as a unit charges or is charged in assault, it loses all its pins automatically.
If there is no obstacle between the assaulters and the target, then the assaulting units gets to roll its dice first. If there is an obstacle however, then both units get to roll simultaneously...so hiding behind a fence or wall is great if the enemy is charging you!
To attack, each model gets 1 dice if equipped normally, and 2 dice if equipped with an assault weapon (ARs, SMG, Pistol) Some Unit Special Rules grant an extra dice in close combat which can be very nasty (you don't wanna know about Ghurkas....)
There is no 'to hit' roll in close combat, you simply need to roll the target units Kill value (ie 5+ for Vets, 4+ for Regs etc) Every dice that comes up with this number or higher removes one enemy model.
Once all participants have had their attacks, the result are compared to see who caused the most casualties, and the loser is wiped out, regardless of the amount of models actually left in the unit. Again, some unit special rules prevent this (Fanatics for example) and allow units to fight on to the bitter end.
The winner then consolidates D6 inches (and can't re-assault that turn)
As far as scenarios go, the 6 in the main BA rulebook range from capture the most objectives, destroy the enemy base, kill everyone and Top Secret, which is a bit of a silly dash for the middle objective and then run the item off your table edge. The tournaments I have been in usually modify these missions somewhat for a more interesting game, but the basic scenarios (bar 1) are quite workable.
In almost all scenarios, you can keep some of your force off table as reserves, and can even outflank down either table edge (left or right) by secretly writing down the units and which side you will bring them on . An orders check on the turn you decide to reveal them allows you to bring the outflankers on 12 inches down the edge for every turn after Turn 1 that you held them off table for...so a unit coming on in Turn 4 will be 36 inches down the side of the table...handy for those right flank attacks! Of course, having to pass an orders check (at a -1, stand fast USA) means there is a chance they will refuse to come one (nav errors) and any units that don't make it onto the table by games end count as destroyed.....
Arty tends to cause pins on multiple units over a wide area, whilst air tends to be more devastating but on a specific target unit....
The different nations that fight have their own Army Books, although the minor allied powers and Minor Axis powers have been grouped together into one book each. Each nation will have from 2-4 Nation specific rules, such as Hitlers Buzzsaw, which reflects the German MG36 and MG42 high rates of fire granting all German LMG and MMG an extra RoF dice, and the US Armies Better Comms which means they don't suffer -1 to leadership when rolling to come on from Reserve, nor do they suffer the -1 to move and shoot due to their M-1 Garand semi-auto rifles. The US also get an extra Air Observer for free if one is bought, hence allowing the US two air strikes a game vice 1, and the Brits have a simliar rule allowing a free Off Board Artillery observer, hence allowing 2 arty strikes per game. The British book also allows the Brit player to pick an extra two rules from a list of 4 or such as extra Assault dice, extra firepower from rifles, stubborn leadership checks etc which the player can use to represent the other Commonwealth countries fighting abilities (Ghurkas, Australians, Indians etc all get to be represented depending how a player wants to assign the extra special rules) Each army book also includes theatre specific list restrictions to reflect the historically available units to allow more accurate match-ups for that nation.