How can I add a vertical scrollbar to my div automatically?

You need to assign some height to make the overflow: auto; property work.

For testing purpose, add height: 100px; and check.

and also it will be better if you give overflow-y:auto; instead of overflow: auto;, because this makes the element to scroll only vertical but not horizontal.

float:left;
width:1000px;
overflow-y: auto;
height: 100px;

If you don’t know the height of the container and you want to show vertical scrollbar when the container reaches a fixed height say 100px, use max-height instead of height property.

For more information, read this MDN article.