Using a Library

If you are doing a lot of date work, you may want to look into JavaScript date libraries like Datejs or Moment.js. For example, with Moment.js, this is simply:

var newDateObj = moment(oldDateObj).add(30, 'm').toDate();

Vanilla Javascript

This is like chaos’s answer, but in one line:

var newDateObj = new Date(oldDateObj.getTime() + diff*60000);

Where diff is the difference in minutes you want from oldDateObj‘s time. It can even be negative.

Or as a reusable function, if you need to do this in multiple places:

function addMinutes(date, minutes) {
    return new Date(date.getTime() + minutes*60000);
}

^{And just in case this is not obvious, the reason we multiply minutes by 60000 is to convert minutes to milliseconds.}

Be Careful with Vanilla Javascript. Dates Are Hard!

You may think you can add 24 hours to a date to get tomorrow’s date, right? Wrong!

addMinutes(myDate, 60*24); //DO NOT DO THIS

It turns out, if the user observes daylight saving time, a day is not necessarily 24 hours long. There is one day a year that is only 23 hours long, and one day a year that is 25 hours long. For example, in most of the United States and Canada, 24 hours after midnight, Nov 2, 2014, is still Nov 2:

const NOV = 10; //because JS months are off by one...
addMinutes(new Date(2014, NOV, 2), 60*24); //In USA, prints 11pm on Nov 2, not 12am Nov 3!

This is why using one of the afore-mentioned libraries is a safer bet if you have to do a lot of work with this.

Below is a more generic version of this function that I wrote. I’d still recommend using a library, but that may be overkill/impossible for your project. The syntax is modeled after MySQL DATE_ADD function.

/**
 * Adds time to a date. Modelled after MySQL DATE_ADD function.
 * Example: dateAdd(new Date(), 'minute', 30)  //returns 30 minutes from now.
 * https://stackoverflow.com/a/1214753/18511
 * 
 * @param date  Date to start with
 * @param interval  One of: year, quarter, month, week, day, hour, minute, second
 * @param units  Number of units of the given interval to add.
 */
function dateAdd(date, interval, units) {
  if(!(date instanceof Date))
    return undefined;
  var ret = new Date(date); //don't change original date
  var checkRollover = function() { if(ret.getDate() != date.getDate()) ret.setDate(0);};
  switch(String(interval).toLowerCase()) {
    case 'year'   :  ret.setFullYear(ret.getFullYear() + units); checkRollover();  break;
    case 'quarter':  ret.setMonth(ret.getMonth() + 3*units); checkRollover();  break;
    case 'month'  :  ret.setMonth(ret.getMonth() + units); checkRollover();  break;
    case 'week'   :  ret.setDate(ret.getDate() + 7*units);  break;
    case 'day'    :  ret.setDate(ret.getDate() + units);  break;
    case 'hour'   :  ret.setTime(ret.getTime() + units*3600000);  break;
    case 'minute' :  ret.setTime(ret.getTime() + units*60000);  break;
    case 'second' :  ret.setTime(ret.getTime() + units*1000);  break;
    default       :  ret = undefined;  break;
  }
  return ret;
}

Working jsFiddle demo.