When the battle starts, your troops have already been deployed for you. In a lot of scenarios you will receive reinforcements. As they arrive on the board, they will appear on the respective roads, usually in march column.

They will move several hexes into the battlefield, unless enemy units are close by. In this case they will enter several hexes away in order to avoid the enemy (as they are in march column and quite vulnerable).

For some scenarios reinforcement brigades do not always turn up on the same turn every time you fight the same battle. After a battle has started, you can always tell exactly what turn any brigade is going to turn up for the battle by selecting the brigade in the order of battle. However, this will not be the same every time you fight the same battle. There is a chance that some of the brigades are late to the battle.