There are many ways to customize the look of the search box using CSS. Heather Solomon's CSS Chart provides a handy reference for these settings and others. There are a few areas it does not address.
One item that you cannot change is the width of the text input box. For some reason the width for this box is hardcoded as a style tag right in the input tag. It is set to 170px. This is unfortunate as a smaller text input field would help my layout.
If you are looking to hide the Advanced Search link, you can do that. Read this post for more information.
