Amphibious warfare ships will have an icon on them that looks like a truck driving through some water on the unit stats (left side of the stats). These are usually ships like LHDs, LCT's and some carriers (so check both carriers and transport ships).
Well, if you have amphib transports, select your units, right click on the ship you want to load them into, and press load into, let the ship and the units move to the nearest port and they will go into the ship (once you give the load into order, they will move to the port automatically), then move your ship near the enemy coast and with the ship selected, right click on a land hex where you want them landed, and select unload, and the ship will mvoe there and unload them. You do not need a sea pier or port in that hex to land them.
If you don't have amphib transports, you will have to clear a hex out that has a pier or port, and then use your transport, and tell it to unload at the hex with the sea pier (it should work)