How to add a class to a given element?

If you're only targeting modern browsers:

Use element.classList.add to add a class:

element.classList.add("my-class");

And element.classList.remove to remove a class:

element.classList.remove("my-class");

If you need to support Internet Explorer 9 or lower:

Add a space plus the name of your new class to the className property of the element. First, put an id on the element so you can easily get a reference.

<div id="div1" class="someclass">
    <img ... id="image1" name="image1" />
</div>

Then

var d = document.getElementById("div1");
d.className += " otherclass";

Note the space before otherclass. It's important to include the space otherwise it compromises existing classes that come before it in the class list.

See also element.className on MDN.

The easiest way to do this without any framework is to use element.classList.add method.

var element = document.getElementById("div1");
element.classList.add("otherclass");

Edit: And if you want to remove class from an element -

element.classList.remove("otherclass");

I prefer not having to add any empty space and duplicate entry handling myself (which is required when using the document.className approach). There are some browser limitations, but you can work around them using polyfills.