I had a server with a manual installation (local compilation -> ./configure && make; make install) of Ruby v1.9.2 and I needed to upgrade this to v1.9.3 - How did I do this?
Technically I didn't... it worked out to be too much hassle long term to upgrade the manual installation on a production server so I installed Ruby Version Manager over the top which overwrote the underlying links to the previous version of Ruby. I believe it is best practise to use a version manager for Ruby such as RVM which not only allows you to manage Ruby versions server-wide but also per-project versions and gemsets.
The steps I took to install and use RVM were as follows:
rvm installwhich ever Ruby versions you require
And thats it, also in future it is really easy to upgrade again by just letting RVM do the hard work.