Ah, this is a post of just blah blah and no code at all, but I think it would be helpful to write down all I know about Oracle database patching.
First of all, I'll assume that you have a good reason to patch an Oracle database because not all the patches released are trouble-free, therefore sometimes the fix is worse than the bug. If you can, check a patch in a test database or at least wait some time to see what other people got applying that patch.
Next, it is necessary to have a Metalink account and rights to download patches; having a Metalink account is not enough, and your company has to have an Oracle support contract in order to grant you access to Metalink patches. But there are support contracts and support contracts; if you think that having a Premier Support contract entitles you to download all the patches you would ever need it might be better to read the Metalink article How Patches and Updates Entitlement Works. If you can't get a patch (by Metalink or otherwise), then it's almost useless to know what the current patch is.
Oracle patch information is somewhat difficult to understand, but if you need to know information about patch releases you can check the Critical Patch Updates and Security Alerts page. Here in the Critical Patch Updates section you can learn when is going to be released the next patch (every three months), and you can also subscribe to the RSS feed or email list in order to get this information automatically.
And in the Security Alerts section you will know if there is an outstanding patch for some serious security bug; if you see a security alert after the last patch release it might be worth checking it an applying the patch, but if you can wait for the next patch release it will be included there.
Then, if you keep following the links you will get detailed information about patches, but if you just want to know what the latest PSU is it would be easier to check the Metalink document Oracle Recommended Patches -- Oracle Database; this way you can get quickly the last patch for your database release. And if you want to know which patch is for what release, you can check it in the Metalink document Quick Reference to Patchset Patch Numbers. Finally, if you want to upgrade your database from version X to version Y and you're not sure, it would be helpful to check the Oracle Database Upgrade Path Reference List.
I hope this information will be helpful for someone; as far as I know this knowledge is not included in any Oracle Database certification test even being so important, and there is not a lot books dealing with this.