how easy is it to unlock an iPhone 4s on EE network and how much does it cost?

ONLY the carrier to which it is locked can unlock it. No one else.

Contact that carrier and ask if they offer this service and if you qualify

Extremely difficult ,the most difficult of all UK carriers to deal with on unlocking

This is the process that should be followed ,they will likely tell you something different

http://support.apple.com/kb/HT5014?viewlocale=en_US

and this for EE

http://ee.co.uk/help/getting-started/joining-ee/unlocking-your-phone#ee