let unix_timestamp = 1549312452;

// Create a new JavaScript Date object based on the timestamp
// multiplied by 1000 so that the argument is in milliseconds, not seconds
var date = new Date(unix_timestamp * 1000);

// Hours part from the timestamp
var hours = date.getHours();

// Minutes part from the timestamp
var minutes = "0" + date.getMinutes();

// Seconds part from the timestamp
var seconds = "0" + date.getSeconds();

// Will display time in 10:30:23 format
var formattedTime = hours + ':' + minutes.substr(-2) + ':' + seconds.substr(-2);

console.log(formattedTime);

For more information regarding the Date object, please refer to MDN or the ECMAScript 5 specification.

Split the string into its parts and provide them directly to the Date constructor:

Update:

var myDate = "26-02-2012";
myDate = myDate.split("-");
var newDate = new Date( myDate[2], myDate[1] - 1, myDate[0]);
console.log(newDate.getTime());

Updated: Also, you can use a regular expression to split the string, for example:

const dtStr = "26/02/2012";
const [d, m, y] = dtStr.split(/-|\//); // splits "26-02-2012" or "26/02/2012"
const date = new Date(y, m - 1, d);
console.log(date.getTime());

Timestamp in milliseconds

To get the number of milliseconds since Unix epoch, call Date.now:

Date.now()

Alternatively, use the unary operator + to call Date.prototype.valueOf:

+ new Date()

Alternatively, call valueOf directly:

new Date().valueOf()

To support IE8 and earlier (see compatibility table), create a shim for Date.now:

if (!Date.now) {
    Date.now = function() { return new Date().getTime(); }
}

Alternatively, call getTime directly:

new Date().getTime()

Timestamp in seconds

To get the number of seconds since Unix epoch, i.e. Unix timestamp:

Math.floor(Date.now() / 1000)

Alternatively, using bitwise-or to floor is slightly faster, but also less readable and may break in the future (see explanations 1, 2):

Date.now() / 1000 | 0

Timestamp in milliseconds (higher resolution)

Use performance.now:

var isPerformanceSupported = (
    window.performance &&
    window.performance.now &&
    window.performance.timing &&
    window.performance.timing.navigationStart
);

var timeStampInMs = (
    isPerformanceSupported ?
    window.performance.now() +
    window.performance.timing.navigationStart :
    Date.now()
);

console.log(timeStampInMs, Date.now());