How to add/subtract dates with JavaScript?

I want to let users easily add and subtract dates using JavaScript in order to browse their entries by date.

The dates are in the format: "mm/dd/yyyy". I want them to be able to click a "Next" button, and if the date is: " 06/01/2012" then on clicking next, it should become: "06/02/2012". If they click the 'prev' button then it should become, "05/31/2012".

It needs to keep track of leap years, number of days in the month, etc.

Any ideas?

P.S using AJAX to get the date from the server isn't an option, its a bit laggy and not the experience for the user that the client wants.

Code:

var date = new Date('2011', '01', '02');
alert('the original date is ' + date);
var newdate = new Date(date);

newdate.setDate(newdate.getDate() - 7); // minus the date

var nd = new Date(newdate);
alert('the new date is ' + nd);

Using Datepicker:

$("#in").datepicker({
    minDate: 0,
    onSelect: function(dateText, inst) {
       var actualDate = new Date(dateText);
       var newDate = new Date(actualDate.getFullYear(), actualDate.getMonth(), actualDate.getDate()+1);
        $('#out').datepicker('option', 'minDate', newDate );
    }
});

$("#out").datepicker();​

JSFiddle Demo

Extra stuff that might come handy:

getDate()   Returns the day of the month (from 1-31)
getDay()    Returns the day of the week (from 0-6)
getFullYear()   Returns the year (four digits)
getHours()  Returns the hour (from 0-23)
getMilliseconds()   Returns the milliseconds (from 0-999)
getMinutes()    Returns the minutes (from 0-59)
getMonth()  Returns the month (from 0-11)
getSeconds()    Returns the seconds (from 0-59)

Good link: MDN Date

You need to use getTime() and setTime() to add or substract the time in a javascript Date object. Using setDate() and getDate() will lead to errors when reaching the limits of the months 1, 30, 31, etc..

Using setTime allows you to set an offset in milliseconds, and let the Date object figure the rest:

var now=new Date();
var yesterdayMs = now.getTime() - 1000*60*60*24*1; // Offset by one day;
now.setTime( yesterdayMs );

startdate.setDate(startdate.getDate() - daysToSubtract);


startdate.setDate(startdate.getDate() + daysToAdd);