Updated Bootstrap 3.x
You can use the .input-group class like this:
<div class="input-group">
<input type="text" class="form-control"/>
<span class="input-group-addon">
<i class="fa fa-search"></i>
</span>
</div>
Working Demo in jsFiddle for 3.x
Bootstrap 2.x
You can use the .input-append class like this:
<div class="input-append">
<input class="span2" type="text">
<button type="submit" class="btn">
<i class="icon-search"></i>
</button>
</div>
Working Demo in jsFiddle for 2.x
Both will look like this:
If you'd like the icon inside the input box, like this:
Then see my answer to Add a Bootstrap Glyphicon to Input Box