Depends entirely on your situation.
Is your site unresponsive or slow at the moment? Is this definitely due to the PHP scripts and not any other data sources such as a database or remote API?
If you answered yes to the above, then installing one of the many PHP accelerators out there would be a good shout. As for using less memory, that's largely dependent on your apache/lightppd/nginx config and php.ini variables.
Most PHP accelerators work by converting the (to be) interpreted PHP code into opcode. This is then stored in memory (RAM) for fast access. If you haven't already implemented file-based caching in CodeIgniter then the benefits of installing a PHP accelerator would be noticeable. If you haven't, then I suggest you do that first before moving straight over to (wasting?) spending time trying to install APC manually.
If your site is currently performing well and you're not too confident in your *nix skills then I suggest you try implementing CodeIgniter caching first rather than try messing with what is an already working VPS.
My personal preference is PHP eAccelerator.
Should installing a PHP cache engine not improve your site's performance then I suggest you look at what other factors influence your application. As stated above, these could be: database or API to name a few.
Hope this helps.