How can I reverse an array in JavaScript without using libraries?

Javascript has a reverse() method that you can call in an array

var a = [3,5,7,8];
a.reverse(); // 8 7 5 3

Not sure if that's what you mean by 'libraries you can't use', I'm guessing something to do with practice. If that's the case, you can implement your own version of .reverse()

function reverseArr(input) {
    var ret = new Array;
    for(var i = input.length-1; i >= 0; i--) {
        ret.push(input[i]);
    }
    return ret;
}

var a = [3,5,7,8]
var b = reverseArr(a);

Do note that the built-in .reverse() method operates on the original array, thus you don't need to reassign a.

Array.prototype.reverse() is all you need to do this work. See compatibility table.

var myArray = [20, 40, 80, 100];
var revMyArr = [].concat(myArray).reverse();
console.log(revMyArr);
// [100, 80, 40, 20]