We have installed node.js and npm onto all shared hosting servers.
At the point of writing this is
Node version v0.10.40
npm version 1.4.28
These binaries are located in
/usr/bin
making ......
/usr/bin/node
/usr/bin/npm
To use these you will need to contact support to have SSH enabled on your account for node access, then you can launch node against your node.js code eg
cd /home/myuser/public_html/
/usr/bin/node index.js
This will then start node.
You will then need to use apache's mod_rewrite to proxy port 80 from apache to your local application port, this can be achieved using the following lines in a .htaccess file
RewriteRule ^$ http://127.0.0.1:61000/ [P,L]
replacing 61000 with the port that your node application has created.