The UNI Search module creates a block with a global UNI search using the Google Custom Search Engine.
Install module as normal. A UNI Search block will be available at the Blocks administration page, at Structure > Blocks.
If you're using a sub theme built from unibasetheme, you may add this block to the branding region and it will automatically be floated to the right in the purple header. It is positioned so it does not inhibit the site name.