Here's the look they wanted (nothing really fancy, as you can see):
Here's the CSS:
<style>
#WebPartWPQ2 #SearchBox {
width: 650px;
}
#WebPartWPQ2 .ms-srch-sbLarge > .ms-srch-sb-searchLink {
background-color: #fff;
float: right;
color: #fff;
text-decoration:none;
height: 24px;
width: 33px;
}
#WebPartWPQ2 .ms-srch-sbLarge>input {
border: 1px solid black;
border-radius: 5px;
font-size:16px;
height:30px;
width: 600px;
margin: 0px 0px 0px 0px;
padding: 5px 1%;
}
#WebPartWPQ2 .ms-srch-sbLarge-searchImg {
position: relative;
}
</style>
NOTE: I'm specifically targeting their web part's ID, WebPartWPQ2; therefore, you'll want to change that to reflect the ID of you web part or remove it if you want all Search Boxes to inherit that particular look.