Download latest source tarball, and untar it:
tar xfz stable-snapshot.tar.gz
You will most likely want to add openssl support. You can choose to statically compile in all dependencies, but this means you have to be sure to re-build your rubies if openssl security vulnerabilities are found (like Heartbleed).
yum -y install openssl-devel
Now we'll enter the directory of the stable-snapshot.tar.gz, configure and install it. When configuring, we'll add an option for SSL (if you skipped that part, you can omit this flag). By default it's installed to /usr/local/, we'll change that and install to /opt/ruby/rbYYYYmmddHHMM. I like to timestamp my builds so I know when they're from. You can create an RPM for this, or recursively copy or rsync it to another folder specific to an app (rails site for example), and then create an RPM specific to that environment. Here, we'll just use the datestamp.
./configure --with-openssl-dir=/usr/lib64/openssl --prefix=/opt/ruby/rb`date +%Y%m%d%H%M`
Now to compile, we simply run make and pay attention to the output.
make && make install
Say this was built with timestamp 201412071746, your freshly-compiled ruby is installed to /opt/ruby/rb201412071746/.
We can set this ruby bin directory in our environment's PATH to avoid typing the entire path. By placing it first, the commands (ruby, gem, etc.) will match here first before finding the system's RUBY in /usr/bin.