I find it very fiddly to embark and disembark, sometimes the ship just refuse to approach the land! does the landing site have to be allied land with a port facility or something...? And sometimes i click the troop to move toward ship and they eventually do board the vessel, but clicking embark does nothing at all. Its very frustrating and fiddly especially combined with the huge slowdown. makes me wish it was turn based because i lose some conflicts trying to transport troops and clicking again and again to transport them on ships but by the time they eventually (if ever) board and disembark I've missed the battle and lost again! lol i lose enough without shipping megabug!
A fleet can either be in the open waters offshore or docked in port. A fleet can only be docked in a province that you or one of your vassals own a holding in (so you don't need the entire province, just one of it's subholdings - even a trade post if you're a republic will do).
The embark button is for moving troops into a docked fleet (instantaneously). It does not work with offshore fleets, which you need to order your troops to march into or off of.