I have SharePoint 2010 project which consists of a group of webparts, I need to make it work on 2013, what should I do? Can I just deploy it right away? Are there any thing i have to do?

You need to open the solution in VS 2012-2013, update the reference to layouts, and control templates, and reference to the assembly, make sure it compiles, buildable, and try it out on test environment.