A general introduction to the PeoplePicker widget is available from Microsoft.
A reliable way to find a user registered in SharePoint is to type in his last name (family name) or a part of it (without "joker characters" like asterisk '*'). However there may be multiple matches in the user database, and a red text will indicate "No exact match was found for XXX.", XXX being the search term.
As an example (see window screen shot at the left), the search for "benbow" yields two matches, and after clicking the check icon (or hitting the return key), the error message instructs the user to click (using the left mouse button) on the term with multiple matches, which triggers a drop-down menu with the possible alternatives.
The example case contains a user name marked "(old)", which is specific to CTA-SharePoint and indicates an account that should not be used, but remains in the database, as long as connections (through earlier created elements) to that account exist.