I'm not sure if you want it spelled out in Korean or want the transliteration, so I'll give you both! 공주 is the most commonly used word for princess. I think the closest transliteration would be gohng-joo. For 'gohng', the closest you could get using sounds in English would be if you combined the word 'go' and the 'ng' sound from 'sing'. For 'joo', just pronounce it like it's spelled but cut the 'oo' sound off shorter than you normally would in English.
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princess:~
*왕녀 : wang-nyeo
*공주 : gwang-joo
*황녀 : hwang-nyeo
*왕가의 여자 : wang-ga-e-yeoja
^_^
I'm not sure if you want it spelled out in Korean or want the transliteration, so I'll give you both! 공주 is the most commonly used word for princess. I think the closest transliteration would be gohng-joo. For 'gohng', the closest you could get using sounds in English would be if you combined the word 'go' and the 'ng' sound from 'sing'. For 'joo', just pronounce it like it's spelled but cut the 'oo' sound off shorter than you normally would in English.
공주 = princess