[bhlloy]

IIRC there's two ways to do it. Either have ships in port and troops in same province and there's a small "load" button somewhere on the army pop-up, or move them into an adjacent sea zone and move them onto the ships. First way is much faster.

EDIT - very possible you don't actually have enough capacity on the ships to embark that many soldiers? In that case the button is greyed out? Looks like an arrow pointing at a ship.

DOUBLE EDIT - 1 ship for 100 soldiers. Thanks Reddit!