@Dean, can you post a link or 2 as a guide please? Noob alert over here
Sure, I've written my own guide below rather than pasting links. I find my way the best for me, so you can either follow that or find one which makes more sense to you if others have some other way
First things first, are you rooted? If not, follow this link for a guide.
Those were the days... these days it's a lot easier than that to root.
Rooting:
Search Google for an app called Framaroot - it's as easy as installing that and touching a button on your phone... done that lately for some mates' S3s.
Flashing Preparation
Download the CM11 Nightly .zip file (assuming you have the i9300 S3, you'd get yours from
http://download.cyanogenmod.org/?device=i9300 - it's about 200MB ) and copy it to your
external MicroSD card in your phone.
Also download the latest CM 11 Google Apps from
http://wiki.cyanogenmod.org/w/Google_Apps - make sure it's the one which as of today is on the top of the list ie. the one for CM11. I use the "It Vends" link on the page since it then downloads in browser rather than over torrents. Copy it to the
external MicroSD in your phone.
While those are busy downloading, install ClockworkMod (CWM) on the phone from PlayStore.
Open CWM app and tap to install CWM Recovery - though I rather suggest at this point buying the in-app purchase CWM
Touch Recovery. The non-touch recovery module is a serious mission to use when it comes to flashing, even though the regular app seems easy to navigate on the phone.. trust me on this one the touch recovery is worth every cent, especially for a first timer.
Image Backup
Switch off your phone. Boot into CWM by holding the following three buttons: VolumeUp, Home and finally Power. You can let go of power once you see the Samsung SGS3 title.
You'll see it boot into a weird-looking interface that you've never seen before - that's CWM. select Backup/Restore and then Backup - this will do a "Nandroid"/Image backup to your MicroSD card... an optional extra step that's always good to do for those unlikely events.
Flashing new ROM
Note: Everything after this point will result in all content on your phone being wiped, so make sure you have all necessary data/info/media backed up or on your external MicroSD card rather than the internal phone memory. All purchased and free apps linked to your Google account can obviously be re-downloaded as before without paying again, and if you've been using a Google linked calendar and contacts, then those will obviously work as before too.
You're now ready for the fun, but quick part. In the CWM menu, select to Install .zip from SD card, and navigate to wherever you saved that CM-Nightly .zip file. Don't worry about unzipping yourself, it does all the work for you. DONT DO ANYTHING ELSE BEFORE MOVING ON TO THE NEXT STEP.
Once it's finished - it only takes a few seconds, do exactly the same for the GApps .zip file on your MicroSD (ie. Install .zip from SD, select GApps...zip). AGAIN, DONT DO ANYTHING ELSE BEFORE MOVING ON TO THE NEXT STEP.
Post-Flash House-keeping
IMPORTANT: Select the option in the CWM menu to Wipe Data/Factory Reset. This must be done at this step, ie. after flashing and not before. As weird as it may initially seem, it will make sense if you care enough to research the reasoning.
Don't think that you can skip this step and have all your stuff still there and avoid having to restore backups or make backups in the first place...it'll just cause chaos.
It's often good at this point to select the options in the CWM menu to clear the cache and Dalvik cache, though it isn't always necessary. Both clearances take seconds though so I like to do regardless.
At this stage you can select in CWM's menu to Reboot the phone and it should start up with the CyanogenMod splash-screen instead of the Samsung logo.. followed by being one of the smoothest S3s around.
Possible Issues
I ran into an issue where the Nightly wouldn't install - it was because I was using version 5.xxx of CWM, and CM11 requires CWM version 6.xxx