use a javascript array to fill up a drop down select box

Use a for loop to iterate through your array. For each string, create a new option element, assign the string as its innerHTML and value, and then append it to the select element.

var cuisines = ["Chinese","Indian"];     
var sel = document.getElementById('CuisineList');
for(var i = 0; i < cuisines.length; i++) {
    var opt = document.createElement('option');
    opt.innerHTML = cuisines[i];
    opt.value = cuisines[i];
    sel.appendChild(opt);
}

DEMO

UPDATE: Using createDocumentFragment and forEach

If you have a very large list of elements that you want to append to a document, it can be non-performant to append each new element individually. The DocumentFragment acts as a light weight document object that can be used to collect elements. Once all your elements are ready, you can execute a single appendChild operation so that the DOM only updates once, instead of n times.

var cuisines = ["Chinese","Indian"];     

var sel = document.getElementById('CuisineList');
var fragment = document.createDocumentFragment();

cuisines.forEach(function(cuisine, index) {
    var opt = document.createElement('option');
    opt.innerHTML = cuisine;
    opt.value = cuisine;
    fragment.appendChild(opt);
});

sel.appendChild(fragment);

DEMO