A JavaScript Date has several methods allowing you to extract its parts:

getFullYear() - Returns the 4-digit year
getMonth() - Returns a zero-based integer (0-11) representing the month of the year.
getDate() - Returns the day of the month (1-31).
getDay() - Returns the day of the week (0-6). 0 is Sunday, 6 is Saturday.
getHours() - Returns the hour of the day (0-23).
getMinutes() - Returns the minute (0-59).
getSeconds() - Returns the second (0-59).
getMilliseconds() - Returns the milliseconds (0-999).
getTimezoneOffset() - Returns the number of minutes between the machine local time and UTC.

There are no built-in methods allowing you to get localized strings like "Friday", "February", or "PM". You have to code that yourself. To get the string you want, you at least need to store string representations of days and months:

var months = ["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"];
var days = ["Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"];

Then, put it together using the methods above:

var months = ["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"];
var days = ["Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"];
var d = new Date();
var day = days[d.getDay()];
var hr = d.getHours();
var min = d.getMinutes();
if (min < 10) {
    min = "0" + min;
}
var ampm = "am";
if( hr > 12 ) {
    hr -= 12;
    ampm = "pm";
}
var date = d.getDate();
var month = months[d.getMonth()];
var year = d.getFullYear();
var x = document.getElementById("time");
x.innerHTML = day + " " + hr + ":" + min + ampm + " " + date + " " + month + " " + year;

<span id="time"></span>

I have a date format function I like to include in my standard library. It takes a format string parameter that defines the desired output. The format strings are loosely based on .Net custom Date and Time format strings. For the format you specified the following format string would work: "dddd h:mmtt d MMM yyyy".

var d = new Date();
var x = document.getElementById("time");
x.innerHTML = formatDate(d, "dddd h:mmtt d MMM yyyy");

Demo: jsfiddle.net/BNkkB/1

Here is my full date formatting function:

const MMMM = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"];
const MMM = MMMM.map(m => m.slice(0, 3));
const dddd = ["Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"];
const ddd = dddd.map(d => d.slice(0, 3));

function ii(i, len = 2) {
    return (i + "").padStart(len, "0");
}

function tzHHMM(tz) {
    const sign = tz > 0 ? "-" : "+"; // +08:00 == -480, signs are reversed
    const tzv = Math.abs(tz);
    const tzHrs = Math.floor(tzv / 60);
    const tzMin = tzv % 60;
    return sign + ii(tzHrs) + ":" + ii(tzMin);
}

function formatDate(date, format, utc) {
    const y = utc ? date.getUTCFullYear() : date.getFullYear();
    const M = utc ? date.getUTCMonth() : date.getMonth();
    const d = utc ? date.getUTCDate() : date.getDate();
    const H = utc ? date.getUTCHours() : date.getHours();
    const h = H > 12 ? H - 12 : H == 0 ? 12 : H;
    const m = utc ? date.getUTCMinutes() : date.getMinutes();
    const s = utc ? date.getUTCSeconds() : date.getSeconds();
    const f = utc ? date.getUTCMilliseconds() : date.getMilliseconds();
    const TT = H < 12 ? "AM" : "PM";
    const tt = TT.toLowerCase();
    const day = utc ? date.getUTCDay() : date.getDay();
    const replacements = {
        y,
        yy: y.toString().slice(-2),
        yyy: y,
        yyyy: y,
        M,
        MM: ii(M),
        MMM: MMM[M],
        MMMM: MMMM[M],
        d,
        dd: ii(d),
        ddd: ddd[day],
        dddd: dddd[day],
        H,
        HH: ii(H),
        h,
        hh: ii(h),
        m,
        mm: ii(m),
        s,
        ss: ii(s),
        f: Math.round(f / 100),
        ff: ii(Math.round(f / 10)),
        fff: ii(f, 3),
        ffff: ii(f * 10, 4),
        T: TT[0],
        TT,
        t: tt[0],
        tt,
        K: utc ? "Z" : tzHHMM(date.getTimezoneOffset()),
        "\\": "",
    };
    return format.replace(/(?:\\(?=.)|(?<!\\)(?:([yMdf])\1{0,3}|([HhmsTt])\2?|K))/g, $0 => replacements[$0]);
}

For custom-delimited date formats, you have to pull out the date (or time) components from a DateTimeFormat object (which is part of the ECMAScript Internationalization API), and then manually create a string with the delimiters you want.

To do this, you can use DateTimeFormat#formatToParts. You could destructure the array, but that is not ideal, as the array output depends on the locale:

{ // example 1
   let formatter = new Intl.DateTimeFormat('en');
   let example = formatter.formatToParts();
   console.log(example);
}
{ // example 2
   let formatter = new Intl.DateTimeFormat('hi');
   let example = formatter.formatToParts();
   console.log(example);
}

Better would be to map a format array to resultant strings:

function join(date, options, separator) {
   function format(option) {
      let formatter = new Intl.DateTimeFormat('en', option);
      return formatter.format(date);
   }
   return options.map(format).join(separator);
}

let options = [{day: 'numeric'}, {month: 'short'}, {year: 'numeric'}];
let joined = join(new Date, options, '-');
console.log(joined);

You can also pull out the parts of a DateTimeFormat one-by-one using DateTimeFormat#format, but note that when using this method, as of March 2020, there is a bug in the ECMAScript implementation when it comes to leading zeros on minutes and seconds (this bug is circumvented by the approach above).

let date = new Date(2010, 7, 5);
let year = new Intl.DateTimeFormat('en', { year: 'numeric' }).format(date);
let month = new Intl.DateTimeFormat('en', { month: 'short' }).format(date);
let day = new Intl.DateTimeFormat('en', { day: '2-digit' }).format(date);
console.log(`{month}-${year}`);

When working with dates and times, it is usually worth using a library (eg. luxon, date-fns, moment.js is not recommended for new projects) because of the many hidden complexities of the field.

Note that the ECMAScript Internationalization API, used in the solutions above is not supported in IE10 (0.03% global browser market share in Feb 2020).