Non-JavaScript menus are surprisingly common and are often times just as clean and can be more efficient than their JavaScript counterparts. You can use JavaScript but it's important to have graceful degradation if you want your menu to be accessible and functional for all users.
There are many examples of these online but the basic premise is to have a normal navigation menu (using UL and LI elements), and use CSS to change the look and appearance based on the user interaction (such as a hover).
Here is an example of a basic menu that will work without CSS or JavaScript and still be perfectly usable (some of the code taken from this answer: https://stackoverflow.com/a/12279190/937012)
<div class="wrapper">
<navigation role="navigation" class="primary-nav">
<ul role="menubar">
<li role="presentation">
<a role="menu-item" href="#" title="First Link">First Link</a>
</li>
<li role="presentation" class="sub-container"> <a role="menu-item" aria-haspopup="true" href="#" title="Second Link">Second Link</a>
<ul role="menu">
<li role="presentation"> <a role="menu-item" href="#" title="Sub Menu Item 1">Sub Item 1</a>
</li>
<li role="presentation"> <a role="menu-item" href="#" title="Sub Menu Item 2">Sub Item 2</a>
</li>
<li role="presentation"> <a role="menu-item" href="#" title="Sub Menu Item 3">Sub Item 3</a>
</li>
</ul>
</li>
<li role="presentation">
<a role="menu-item" href="#" title="Third Link">Third Link</a>
</li>
</ul>
</navigation>
</div>
As is, this will create a navigation menu (using some accessibility attributes) that is cross-browser and accessible. You can read more about accessibility best practices here: https://www.webaccessibility.com/best_practices.php
You can then apply whichever CSS you like to change the appearance and give the desired "drop-down" effect.
Here is some CSS for the above markup that produces a horizontal menu that features a sub-menu that appears below the second link when the mouse is moved over the second list item.
A {
text-decoration: none;
}
A:HOVER {
color: blue;
}
.wrapper {
width: 90%;
display: block;
}
.primary-nav {
display: block;
margin: 0px auto;
width: 100%;
padding: 0px;
}
.primary-nav UL {
background-color: #ababcd;
list-style-type: none;
margin-left: 0px;
padding-left: 0px;
text-indent: 0px;
}
.primary-nav > UL {
display: inline;
border: solid 1px #000000;
text-indent: 0px;
float: left;
height: 24px;
margin: 0px;
width: 100%;
list-style-type: none;
border-collapse: collapse;
}
.primary-nav LI {
max-width: 150px;
text-align: center;
}
.primary-nav > UL LI {
display: inline;
float: left;
padding: 0px 3px 0px 3px;
width: 32%;
line-height: 24px;
vertical-align: top;
margin-top: 0px;
text-align: center;
}
.primary-nav > UL LI UL {
display: none;
width: 100%;
}
.primary-nav > UL LI.sub-container:HOVER UL {
display: inline-block;
float: left;
margin-left: 0px;
clear: both;
border: inset 1px #898989;
box-shadow: 2px 2px 4px #000000;
}
.primary-nav > UL LI.sub-container:HOVER UL LI {
margin-top: 2px;
text-align: left;
clear: both;
width: 100%;
padding: 0px;
}
.primary-nav LI A:HOVER {
background-color: #cdcdef;
}
.primary-nav LI A {
display: block;
}
.primary-nav > UL LI.sub-container:HOVER UL LI A {
padding: 1px 3px;
margin: 0px 3px;
}
Here is a fiddle that stitches it all together: http://jsfiddle.net/xDaevax/osu7t9ty/