In order to transport land units across sea zones, a coordinated set of orders must be created. First the transport unit group must be given an order to load cargo from an adjacent land territory. The transport unit group may be given orders to move before being given the order to load. Once the load order is created, the land unit group must be given an order to embark into the sea zone containing the intended transport. Once the embark order is created, the transport unit group and land unit group are bound together. The transport may be given move orders after the unit groups are bound together (as long as the total movement of the transport unit doesn't exceed two zones). Once bound together, the transport unit can be given an order to unload into an adjacent land territory.
If the land unit cargo is unloaded into a territory with enemy units, the unload operation is an "amphibious assault". Since all nations' units are moving simultaneously, it is not possible to predict which unload operations will result in an amphibious assault. Where this happens a conflict occurs, stopping other land units moving into that territory, and a battle ensues, just like any other land territory conflict.
The only difference between an amphibious assault and an ordinary land battle is that with an amphibious assault it is possible to include a Battleship unit that was ordered to bombard that same land territory from the same sea zone as a transport unloading. For a bombard order to be valid, the Battleship must not have participated in sea combat on the same turn. It must also be in the same territory as a friendly transport that is unloading, and the bombard order itself must specify the land territory to which the transport is unloading. It is even possible that multiple nations, even opposing nations, can bombard the same land territory on the same turn, although the Battleships and transports of opposing forces would have to be in different sea zones from each other.