The Calendar class is pretty good for this:
Calendar date = Calendar.getInstance();
^^^ this line sets date with the current date and time
int dayofyear = date.get( Calendar.DAY_OF_YEAR );
^^^ this will give you the number of days that have already past in the current year
date.set( Calendar.MONTH, Calendar.DECEMBER );
date.set( Calendar.DAY_OF_MONTH, 31 );
int lastdayofyear = date.get( Calendar.DAY_OF_YEAR );
^^^ these lines will set date to the last day of the current year, and then return the day number of the last day of the year. this is so you dont have to worry about leapyears.
int daysleft = lastdayofyear - dayofyear;
^^^ just subtract the current day of the year from the last day of the year, and there you are
Hope this helps