You don't have to produce the transport ships. Units automatically embark / convert to transport ships, when sent to sea and automatically back when they finished their disembarkation.
Browser games are an ingenious business idea to lure out money -
- more or less cleverly camouflaged as a real game sometimes.
So beware of caltrops, spring-guns and booby traps.
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Finally got the hang of it! ... Declaration of war required before disembarking ... It seems that it takes over an hour to either embark or disembark, a realistic figure in the real world if an army regiment is doing so! ... Fortunately I had good air and naval support to protect troops from the enemy ... Thanks for the help guys!