In particular, you can look at the getHours() method for the Date object.
getHours() return the time from 0 - 23, so make sure to deal with it accordingly. I think 0-23 is a bit more intuitive since military time runs from 0 - 23, but it's up to you.
With that in mind, the code would be something along the lines of:
var date = new Date();
var current_hour = date.getHours();
Both prior answers are definitely good solutions. If you're amenable to a library, I like moment.js - it does a lot more than just getting/formatting the date.
var date = new Date();
var year = date.getFullYear();
var month = date.getMonth() + 1;
month = (month < 10 ? "0" : "") + month;
var hour = date.getHours();
hour = (hour < 10 ? "0" : "") + hour;
var day = date.getDate();
day = (hour > 12 ? "" : "") + day - 1;
day = (day < 10 ? "0" : "") + day;
x = ":"
console.log( month + x + day + x + year )
It will display the date in the month, day, then the year