JavaScript's dates can be compared using the same comparison operators the rest of the data types use: >, <, <=, >=, ==, !=, ===, !===.
If you have two dates A and B, then A < B if A is further back into the past than B.
But it sounds like what you're having trouble with is turning a string into a date. You do that by simply passing the string as an argument for a new Date:
var someDate = new Date("12/03/2008");
or, if the string you want is the value of a form field, as it seems it might be:
var someDate = new Date(document.form1.Textbox2.value);
Edit:
Should that string not be something that JavaScript recognizes as a date, you will still get a Date object, but it will be "invalid". Any comparison with another date will return false. When converted to a string it will become "Invalid Date". Its getTime() function will return NaN, and calling isNaN() on the date itself will return true; that's the easy way to check if a string is a valid date.