Last night I spent a couple hours figuring this out and other people seemed to be interested, so here you guys go. Sadly, this isn't as simple as it used to be with just adding values to GamePermanent.cfg or anything.
1) Download RAF Manager (http://www.itzwarty.com/bin.zip)
2) Extract to wherever, run RAFManager.exe and point it to your LoL base folder
3) Scroll down on the left column, and locate 0.0.0.87
4) Expand and navigate to /DATA/CFG/defaults/
5) Right click and choose Dump on FontDescriptions.xml and FontResolutions.xml
6) Open these two files in your text editor of choice (I use Notepad++)
FontResolutions.xml is a list of the various font sizes (they incorporate auto sizing and fixed sized ones) and are pretty self expanitory for what they do. For example, "25_4_Auto" would be a base size of 25, outline of 4, and automatic sizing based on resolution. You shouldn't need to modify this file unless you want to add some new font sizes in between or bigger than the ones already in there, but it's good to have a reference of the valid defined font resolutions.
FontDescriptions.xml contains all of the details regarding the various named font aliases used by the game referenced by the .cfg files. For example, the new combat text under PhysicalDamage, MagicalDamage, and TrueDamage. You can modify the font, size (from the FontResolutions.xml file), style, color, etc with this file.
If you'd like to increase the font size, it's as simple as changing the resolution tags from say, 25_3_Auto to 36_4_Auto (this is what I did). You can update the combat text for self and enemy, healing/mana changes, gold/experience numbers, and various other text that shows on champions.
If there's any interest, I'll pastebin the FontDescriptions.xml I ended up using after testing for a while at my resolution (1920x1080) when I get home from work. I ended up increasing the majority of the various fonts by ~50%.
So once you've updated one or both of these .xml files, save them and continue with the following steps.
7) Make sure you're still in the same directory you dumped the files from
8) Drag over the file(s) into the blank right side of the window
9) Name the "mod" whatever (I just used Damage Text)
10) Right click the mod and choose Pack this file
It should automatically back up the original .xml files and overwrite with your custom ones. Launch the game and you should see your changes immediately. If you want to revert to the default, all you have to do is open RAF Manager again and right click the mod and choose Forget.
Disclaimer: This patch has been out less than a day. This fix may need to be re-applied every time the client updates. There is almost zero chance of breaking anything as it is just text file modification but all changes to your game files are done at your own risk.
Enjoy folks, and please bump if it helped you out.