How do you get a current date? Using new Date(); Date is from package java.util.
Date currentDate = new Date();
System.out.println("current date: " + currentDate);
How do you get a current day? You could use getDay() method, but this method was deprecated long time ago and nowadays you should use Calendar:
GregorianCalendar calendar = new GregorianCalendar();
// for current date you don't have to set time
calendar.setTime(currentDate);
System.out.println("current day: " + calendar.get(Calendar.DATE));
How to get the next day? Using Calendar:
calendar.add(Calendar.DATE, 1);
System.out.println("next day: " + calendar.get(Calendar.DATE));
In Calendar class are lots of methods, see Javadoc.
Often you want to convert a date object to String using some pattern. Use class SimpleDateFormat. See Javadoc for patterns:
String txtDate = new SimpleDateFormat("dd/MM/yyyy").format(currentDate);
System.out.println("current date: " + txtDate);
And of course you can convert a String to date object:
Date firstJanuary = new SimpleDateFormat("dd/MM/yyyy").parse("01/01/2013");
System.out.println("first january: " + firstJanuary);