hello,
your question is a bit broad. I will try to reply with the best of my ability.
CRM 2011 to 2013 is a bit tricky because of the changes made in .net framework, JavaScript etc. So any out of the box features like the views, forms etc will upgrade will out much issue.
based on the framework used, your custom buttons, custom workflow activities etc may need some tweaking.
easiest option would be to take a CRM 2011 database backup, restore it as a new SQL server database, use organization import wizard to convert it to a CRM 2013 instance.
the above step assumes that the plugin and JavaScript is already covered by the programmers.
let me know if you have any questions.
Jithesh