There are various ways to do this. It's best to have both divs inside a container, even if set to width: 100%
.
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<style media="all">
.container {position: relative;}
#fixed
{
width: 300px;
height: 100px;
background: #111;
position: absolute;
top: 0; left: 0;
}
#fluid
{
height: 100px;
background: #555;
margin-left: 300px;
}
</style>
</head>
<body>
<div class="container">
<div id="fluid"></div>
<div id="fixed"></div>
</div>
</body>
</html>
A modern option is to use flexbox, but it's not reliably supported yet.