I\'ve been having some issues installing Jekyll on Ubuntu. Here are some of the versions I have:
trevor~$ ruby -v
ruby 2.2.4p230 (2015-12-16 revision 53155)
The error you are getting says it all ERROR: Error installing jekyll: jekyll requires Ruby version >= 2.0.0. You need a version of Ruby that is at least 2.0.0 or greater. I always recommend the latest version unless you need a different version for a specific reason.
So what you need to do is to compile a newer version of ruby. I recommend the latest version 2.3.0. You can download it from ruby-lang.org/en/download. Compiling isn't as hard as everyone says it is, there is a great write up from Compiling Easy HowTo. Once you have it compiled you should be able to install jekyll with the gem and get it up and running. If you have any problems or get any errors come back and I will do my best to help you.