It might be on by default, I can never be sure, but you should do the following anyway:
1> Find your user directory. In Windows 7, that'll be My Documents/My Games/Sid Meier's Civilization V/. Other operating systems might be different, but it shouldn't be too hard to find.
2> In that file is the Logs directory (containing these log files), Maps, MODS, and so on. It's a good idea to know where all of these are, for later use. But also in this directory is a file named "config.ini". Open this; it's raw text, so notepad works fine.
3> A few lines in is "EnableTuner=0". Turn that to a 1 if you ever want to use FireTuner (which you will at some point).
4> About two-thirds of the way down the file, you'll see "LoggingEnabled=0" or something similar. Change that to a 1. Then, look for every other line in that file with the word "Log" or "Logging" involved; if any of those sound interesting, turn them on as well. There are a lot of these; Event logging, AI decision logging, et cetera.
5> Run the game. Some of the files, like Database.log, seem to be mainly generated at the point you load the game, but others, like xml.log, are generated when a mod is activated. Lua.log is simply a text dump of every FireTuner message, which means it's constantly being added to.