SINGULAR
  
 nominative             ἡ    ναῦς   καλή ἐστιν.
 genitive  οὐκέτι ὁρῶ τὰ     τῆς    νεὼς     ἱστία
 dative  προσχωρῶ   τῇ    νηί   
 accusative  ὁρῶ     τὴν    ναῦν    
 vocative   ὦ      ναῦ     take me safely across the sea!
  
PLURAL
  
 nominative          αἱ    νῆες     ἱστία ἔχουσιν
 genitive γιγνώσκομεν τὰ     τῶν    νεῶν     ὀνόματα. (their names * )
 dative  προσχωροῦμεν   ταῖς    ναυσί     
 accusative   θαυμάζω     τὰς    ναῦς    
 vocative   ὦ      νῆες    take us safely across the seas!
  
 
* Like the famous "La Pinta, La Niña y La Santa María", the 3 ships in which Christopher Columbus set out from Spain to find a shorter route to India. And ended up discovering America.

These forms look worse than they actually are:
  • nom sg, voc sg, acc sg and pl, as well as dat pl all have αυ 
    •  ἡ ναῦς 
    •  ὦ ναῦ 
    •  τὴν ναῦν 
    •  τὰς ναῦς 
    •  ταῖς ναυσί 
  • the genitive should have have been τῆς νηός that is why we have, quite regularly
    •  τῇ νηί  (doesn't need a diaeresis. Why not?)
    •  αἱ νῆες 
    •  ὦ νῆες 
  • So what about the genitive case? For the sake of easier pronunciation there has been an inversion of long and short sounds: long η has become short ε. To compensate short ο has turned into long ω. And genitive plural follows suit.
    •  τῆς νεώς 
    •  τῶν νεῶν 
Understanding how forms work is one thing, remembering and applying them automatically is quite a different proposition alltogether. It's only through practicing these forms in meaningful situations that they will soon become familiar and automatic.