Park the transport near a beach or next to the city with a harbor, have the unit that you want to load within moving range of the transport, right click on the transport. This cannot be done next to cliffs, only on beaches/by harbors. If you can't recognize the beach, there is a terrain identifier box that you can turn on in the upper right corner of the screen that tells you what kind of terrain your cursor is over. The cloth map does not show beaches very well, so I suggest scanning the coastline while zoomed in. Also, any city that has a harbor should be able to send troops out with the transport on launch by selecting all the troops and the transport and clicking in the ocean. Troops in the city can be loaded onto a transport by having the transport next to the harbor, selecting the troops in the city, and right-clicking on the transport.

Uhm, I'm having an issue trying to load troops onto a boat in the campaign.  I'm at the point where one of the towns gives you a boat.  I need to load my troops onto it to move down to the next settlement to warn them.  I can load my troops onto the boat.  Then when I move the boat, it just strands the troops in the water...  any clue what's going on here?  What am i missing?  I'd really rather not be forced to move these troops overland... will take forever.  Thanks for any help that you can provide.