The first thing you need to do, after installing the module, is configure Finder's permissions (at admin/user/permissions) so you can control which user roles can use and administer Finder.
Now we will create a Finder. Go to 'Site Building' -> 'Finder' (admin/build/finder). This is the administration page for Finder.
On this page you will have to select a Finder Type. The types of Finders available are determined by which Finder base modules you have enabled. The most common base modules are 'Finder Node', 'Finder Users', and 'Finder Views'. 'Finder Node' and 'Finder Users' integrate directly with Drupal's node and users systems and allow you to create Finders for the basic field values that are associated with these objects in Drupal, such as 'username', 'title', 'node id'. They do not allow you to find values created by other modules such as CCK, Taxonomy, or Profile - for that you will need 'Finder Views'. 'Finder Views' does not find views - it uses one of your existing views to find objects within that view. It does not require 'Finder Node' or 'Finder Users' to work - infact it can find a lot more types of objects and fields from other modules, basically anything that Views can display. Each of these modules creates a corresponding Finder Type you can select from in the list.
Once you have chosen a Finder Type, hit 'Add finder'. You will be presented with the configuration page of the Finder. The most important things here are 'title', 'path' and the checkboxes 'provide block' and 'form on page'. You need to configure the 'title' and 'path' to what you want your users to see - ensure the 'path' is not already in use by something else. Decide whether you want to use a Finder block, and/or have the form on the Finder page. You will see some more options in fieldsets below this, these are defaulted to recommended values. Feel free to browse over them so you know what options are available to you when you want to configure your Finder a little more specifically. Some Finder Types have additional required fields you will need to configure, for example Views finders require you to pick a View from which to find items.
The most important thing a Finder needs is at least one 'element'. These are basically the form elements to put in the Finder form. The types of elements available are determined by element handler modules, which add finder element types like 'autocomplete' in a similar way that the base modules add finder types like 'users'. The element handler modules that come with the Finder package are 'Finder Text', 'Finder Autocomplete', and 'Finder Optionwidgets'. Select a type of element from the list, and hit 'Save finder'.
Now you should be presented with the page to configure the element, where you can choose a title, and which field this Finder will search upon. There are additional options on this page you can browse through, but they are defaulted to usable values. If you change the element type, be sure to double check the element settings, as the options will change depending on the type of element you currently have. When you save a finder element you will be taken back to the configuration page for the Finder you are editing.
To test out your Finder, either activate the block for your Finder (at admin/build/block) or navigate directly to the Finder's path (as can be seen on the Finder administration page).
You can create as many Finders as you like, with as many elements as you need. It is also possible to individually manipulate Finders with various hooks, and theme functions.