How to convert a string of numbers to an array of numbers?

You can use Array.map to convert each element into a number.

var a = "1,2,3,4";

var b = a.split(',').map(function(item) {
    return parseInt(item, 10);
});

Check the Docs

Or more elegantly as pointed out by User: thg435

var b = a.split(',').map(Number);

Where Number() would do the rest:check here

Note: For older browsers that don't support map, you can add an implementation yourself like:

Array.prototype.map = Array.prototype.map || function(_x) {
    for(var o=[], i=0; i<this.length; i++) { 
        o[i] = _x(this[i]); 
    }
    return o;
};

My 2 cents for golfers:

b="1,2,3,4".split`,`.map(x=>+x)

backquote is string litteral so we can omit the parenthesis (because of the nature of split function) but it is equivalent to split(','). The string is now an array, we just have to map each value with a function returning the integer of the string so x=>+x (which is even shorter than the Number function (5 chars instead of 6)) is equivalent to :

function(x){return parseInt(x,10)}// version from techfoobar
(x)=>{return parseInt(x)}         // lambda are shorter and parseInt default is 10
(x)=>{return +x}                  // diff. with parseInt in SO but + is better in this case
x=>+x                             // no multiple args, just 1 function call

I hope it is a bit more clear.