Performing a search in SharePoint is as simple as entering the keyword you want to search for.
This recipe works for:
SharePoint 2010 Foundation
SharePoint 2010 Standard Edition
SharePoint 2010 Enterprise Edition
Office 365 (SharePoint Online)
Basic search is available in all versions of SharePoint, however, with SharePoint Foundation your search scope is limited to only search for content in the site that you are in.
You only need the Read permission level to run a search. However, the results that you see are security trimmed according to the permissions that you have. SharePoint search will not show you items that you do not have permission to see, even if they match your keyword search and exist in SharePoint's search index.
This recipe uses a SharePoint 2010 Team Site for illustration.