Construct a GregorianCalendar with the year, month and day, then query it to find the name of the day. Something like this:
int year = 1977;
int month = 2;
int dayOfMonth = 15;
Calendar myCalendar = new GregorianCalendar(year, month, dayOfMonth);
int dayOfWeek = myCalendar.get(Calendar.DAY_OF_WEEK);
Note that the day of week is returned as an int representing the ordinal of the day in the locale's week day representation. IE, in a locale where the weekday starts on Monday and ends on Sunday, a 2 would represent Tuesday, whereas if the locale weekday starts on Sunday then that same 2 would represent Monday.
Edit
And since there is alot of answer editing going on, allow me to add the following:
DateFormatSymbols symbols = new DateFormatSymbols(Locale.getDefault());
String dayOfMonthStr = symbols.getWeekdays()[dayOfMonth];
Thought to be honest, I like the SimpleDateFormatter approach better, because it encapsulates the very same code as I've shown above. Silly me to forget all about it.