get keys of json-object in JavaScript

[What you have is just an object, not a "json-object". JSON is a textual notation. What you've quoted is JavaScript code using an array initializer and an object initializer (aka, "object literal syntax").]

If you can rely on having ECMAScript5 features available, you can use the Object.keys function to get an array of the keys (property names) in an object. All modern browsers have Object.keys (including IE9+).

Object.keys(jsonData).forEach(function(key) {
    var value = jsonData[key];
    // ...
});

---

The rest of this answer was written in 2011. In today's world, A) You don't need to polyfill this unless you need to support IE8 or earlier (!), and B) If you did, you wouldn't do it with a one-off you wrote yourself or grabbed from an SO answer (and probably shouldn't have in 2011, either). You'd use a curated polyfill, possibly from es5-shim or via a transpiler like Babel that can be configured to include polyfills (which may come from es5-shim).

Here's the rest of the answer from 2011:

Note that older browsers won't have it. If not, this is one of the ones you can supply yourself:

if (typeof Object.keys !== "function") {
    (function() {
        var hasOwn = Object.prototype.hasOwnProperty;
        Object.keys = Object_keys;
        function Object_keys(obj) {
            var keys = [], name;
            for (name in obj) {
                if (hasOwn.call(obj, name)) {
                    keys.push(name);
                }
            }
            return keys;
        }
    })();
}

That uses a for..in loop (more info here) to loop through all of the property names the object has, and uses Object.prototype.hasOwnProperty to check that the property is owned directly by the object rather than being inherited.

(I could have done it without the self-executing function, but I prefer my functions to have names, and to be compatible with IE you can't use named function expressions [well, not without great care]. So the self-executing function is there to avoid having the function declaration create a global symbol.)

var jsonData = [{"person":"me","age":"30"},{"person":"you","age":"25"}];

for(var i in jsonData){
    var key = i;
    var val = jsonData[i];
    for(var j in val){
        var sub_key = j;
        var sub_val = val[j];
        console.log(sub_key);
    }
}

EDIT

var jsonObj = {"person":"me","age":"30"};
Object.keys(jsonObj);  // returns ["person", "age"]

Object has a property keys, returns an Array of keys from that Object

Chrome, FF & Safari supports Object.keys