How can I change the lock screen on my Galaxy Note 2? I got myself a new note 2 last night, and I'm trying to configure it. It's my first android device, so I'm not sure how the system works in some respects.

I came from Windows Phone 7, and there were a few nice features on that phone that I find I'm missing - namely the ability to see upcoming calendar events on my lock screen, as well as the number of emails/texts/whatever I have waiting, and the number of calls that I missed. I found a couple of potential lockscreen apps on google play, but I can't for the life of me figure out how to enable them. There appears to be no option in my settings.

Using android 4.1.2 - don't know if that's the latest version available for me, but I did update last night, presumably from 4.0.
GO Locker has probably the most intuitive interface for changing the lock screen.  Plus they have an embedded store on their application making installation of new themes very easy.  I've noticed in the Google Play Store description for Lockscreen Calendar (not part of GO Locker), that there are reported problems for replacing the lock screen on Samsung devices.  Try Go Locker, that might help override Samsung default settings, then perhaps your own screen locker applications might work.

If your stuck on how to use these applications, try starting them from the Applications menu.  There should be instructions on their use.

NB: Here's a LifeHacker review of Lockscreen Calendar.