Welcome Godot - I'm sure we all want obedient serpents ...
To your question - aboard a ship - all non-pure war ship vessels have a capacity for carrying other ground units -
- Trireme carries two
- Caravel carries 3
- Frigate two
- Galleon four and
- Transport eight units
If a unit is on sentry (sleep) in a port and a vessel leaves that port it will carry the sleeping units aboard it - alternatively you can 'walk' a unit from the shore into an adjacent naval unit for the expense of one movement point. When the ship docks in some other port the sleeping units automatically awaken and can be moved - or if you attempt to move the ship into an unoccupied land square you will be offered the chance to disembark a unit and finally if you click upon a ship carrying units you will be able to individually awaken each unit it carries and move them ashore - into a foreign city or onto another vessel.
You will soon get the hang of it - overseas trade is an important part of most strategies -- of course all the above also works for diplos, spies and military units for somewhat less than peaceful purposes.
Good civin' and, again, Welcome - I hope you enjoy these boards ...