Yesterday's date is simply today's date less one, so:

var d = new Date();

d.setDate(d.getDate() - 1);

If today is 1 April, then it is set to 0 April which is converted to 31 March.

Since you also wanted to do some other stuff, here are some functions to do it:

// Check if d is a valid date

// Must be format year-month name-date

// e.g. 2011-MAR-12 or 2011-March-6

// Capitalisation is not important

function validDate(d) {

  var bits = d.split('-');

  var t = stringToDate(d);

  return t.getFullYear() == bits[0] && 

         t.getDate() == bits[2];

}



// Convert string in format above to a date object

function stringToDate(s) {

  var bits = s.split('-');

  var monthNum = monthNameToNumber(bits[1]);

  return new Date(bits[0], monthNum, bits[2]);

}



// Convert month names like mar or march to 

// number, capitalisation not important

// Month number is calendar month - 1.

var monthNameToNumber = (function() {

  var monthNames = (

     'jan feb mar apr may jun jul aug sep oct nov dec ' +

     'january february march april may june july august ' +

     'september october november december'

     ).split(' ');



  return function(month) {

    var i = monthNames.length;

    month = month.toLowerCase(); 



    while (i--) {

      if (monthNames[i] == month) {

        return i % 12;

      }

    }

  }

}());



// Given a date in above format, return

// previous day as a date object

function getYesterday(d) {

  d = stringToDate(d);

  d.setDate(d.getDate() - 1)

  return d;

}



// Given a date object, format

// per format above

var formatDate = (function() {

  var months = 'jan feb mar apr may jun jul aug sep oct nov dec'.split(' ');

  function addZ(n) {

    return n<10? '0'+n : ''+n;

  }

  return function(d) {

    return d.getFullYear() + '-' + 

           months[d.getMonth()] + '-' + 

           addZ(d.getDate());

  }

}());



function doStuff(d) {



  // Is it format year-month-date?

  if (!validDate(d)) {

    alert(d + ' is not a valid date');

    return;

  } else {

    alert(d + ' is a valid date');

  }

  alert(

    'Date in was: ' + d +

    'nDay before: ' + formatDate(getYesterday(d))

  );

}





doStuff('2011-feb-08');

// Shows 2011-feb-08 is a valid date

//       Date in was: 2011-feb-08

//       Day before: 2011-feb-07