Assuming that the input date is in a format like d/m/y, then you can convert that to a date object using:
function parseDate(s) {
var b = s.split(/\D+/g);
return new Date(b[2], --b[1], b[0]);
}
which creates a date object for 00:00:00 on the specified date.
To compare to the current date, create a new Date object and set the time to 00:00:00.0:
var today = new Date();
today.setHours(0,0,0,0);
Then convert the string to a Date and compare the two:
var otherDay = parseDate('21/4/2013');
console.log(otherDay + ' less than ' + today + '?' + (otherDay < today)); // ... true
Edit
It seems your date format is 4-may-2014. In that case:
function parseDate(s) {
var months = {jan:0,feb:1,mar:2,apr:3,may:4,jun:5,
jul:6,aug:7,sep:8,oct:9,nov:10,dec:12};
var b = s.split(/-/g);
return new Date(b[2], months[b[1].substr(0,3).toLowerCase()], b[0]);
}