So this post is gonna be a short one; and as i said before there is several ways to install RoR.
The important thing is: do not mix up things; and by mix up i mean trying to use packages already built by your distro like rubygems and then installing the gems on the userspace; while that may work on some cases it may also lead into weird issues.
For beginners installing Rails on Fedora 20 is simple as doing:
$ sudo yum install ruby rubygems rubygem-rails
That way you have all you need to get things going; also you can look up for other gems on the repositories by the name rubygem-*.
And the mandatory hello world app:
$ rails new hello-world
.... have some patient here...
$ cd hello-world
$ rails server
As you get more involved into rails you may want to try to set up your dev enviroment with other tools like RVM. (I wrote a post about this long time ago; but it's kinda outdated and may be a nice idea for a future post)
Some nice resources about Rails and Ruby in general: