Think of the ocean 'squares' as provinces with 0 movement costs. Your ships provide a presence in that sea 'province' that allows you to move your troops through with no movement cost. To move troops from one place to another you must first have a port in their origin province and an unbroken path from the origin to the destination.

When you pick up your army, all the valid destination provinces will be highlighted, just like when you pick up an army in a landlocked province.

Be aware that when you drop your army in an enemy province you won't be able to move them back without a port.

Lost your manual, eh? Before you read about ships ... OK.