I'm assuming you are going on a vacaion cruise or flying. Being from Florida I am pretty familiar with the proceedure. At each dock or airport you will need to show your passport and that you have a valid and current visa to be in the USA. I suggest o also carry another form of photo Id such as your driver license and proof that you are currently employed by the employer that sponsored you for the visa. I also strongly suggest that if you are going on a cruise you contact the cruise line and verify with them that you will be able to leave the ship at each dock. Have a good time.
I agree with Ms. Mulder
IMMIGRATION LAW PROFESSOR for 10 years -- LEGAL DISCLAIMER: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship.