Although there are searches on each page there is also a search bar in the left-hand menu. This ties everything into one place and also enables you to use Queries in your searches.
This "omni-search bar" will search all your leads, opportunities, companies and contacts and provide the result broken down as below.
The search is an 'exact' search, so if you entered "Leads365" as your search it will only return items that have a field that is ONLY "Leads365". If you want to search 'begins with', 'ends with' or 'contains' then use the wildcard character (*). So a 'begins with' search would be "Leads365*", 'ends with' is "*Leads365" and contains is "*Leads365*".
Once in this screen you can further narrow down your results by selecting a query from the top left. This will allow you finer control over the exact fields being searched, or searching for multiple arguments.
(To run a query by itself I enter the search screen by doing a "blank" search, i.e. I search for a single wildcard '*').
From here you can also update multiple items at once, for more information please see this article.