How can I setup the search engine to be able to search multiple groups? Users should be able to select what part of my site they want to search.

To allow users to search a particular part of the site, setup Alkaline to index the full site and then add a combo box to the search form that will allow to restrict results to a specific part only.

Use one of the url, path or host options to restrict searching to a particular section of your site.

For example, if you want to search the whole Foo site or just the Bar section, the following form should be added:
<select name="other">
 <option value="">Entire Foo Site</option>
 <option value="url:www.foo.com/bar">Bar Section</option>	
</select>