SharePoint 2010 provide a people search as an out of box feature but you will not find a people search result page on your created site. You must create a new site collection based on Search Center template to find this page.
My problem was I need people search results page on my current site to avoid redirect the user to another site collection
The solution was so simple:
1 – Activate the ShrarePoint Server Enterprise Site Collection feature found on the site features
2 – Add People Search Core Results Web Part found in search category
3- Add a text box and button to redirect to this page with query string “k” which take the value of the your search ex(?k=Mohamed)