What if searching on the web worked the way it did in real life?
Use standard Lijit Wijit
This option will enable the use of the default Lijit Wijit on your blog. Configuration for this Wijit can be done at the Lijit Website (http://www.lijit.com/users/your_username/wijit). After enabling the Wijit in the configuration page the sidebar Wijit needs to be enabled in the WordPress Widget Admin page (/wp-admin/widgets.php). The Lijit Wijit will appear in the list of available widgets. Drag this into your sidebar and save the sidebar. The Wijit will now appear in your site's sidebar.
If your theme is not Widget enabled you can copy and paste the code from the Lijit Options page. In the Search Options section, under the option to use the standard Lijit Wijit there is a link to show the raw code for using the Lijit Wijit. Paste this code into your theme's sidebar.php where you'd like it to appear.
Override WordPress Search Widget
This option will display the default WordPress search field but override its functionality to instead initiate a Lijit search and display the results in a standard Lijit results popup. If you don't already have the WordPress search Widget in your sidebar you will need to add it via the Widget Admin page (/wp-admin/widgets.php). The search widget will appear in the list of available widgets. Drag it into your sidebar and save the sidebar. The search widget will appear in your sidebar and will give Lijit results when used.
If your theme is not Widget enabled there will need to be a standard WordPress search form in your theme's sidebar.php.