Roberto Ierusalimschy's Programming in Lua, 2nd Ed. is an absolute gem. Well written, concise and very authoritative (he's one of the language's co-creators).

One thing worth knowing though: he's working on the 3rd edition (updated for Lua 5.2), though I'm not sure how soon that is expected.

The first edition is online, if you want to get an idea what it's like: http://www.lua.org/pil. In addition, the language's refrence manual is freely available online as well. Depending on how you learn, that would get you started very quickly. (It's a small language and very much follows the principle of least surprise - except for indexing arrays from 1, but you get used to that.) http://www.lua.org/docs.html has the full reference manual for 5.1 and 5.2.

Programming in Lua seems to be the best choice, but mostly by virtue of the very small number of coices. It was most recently printed in 2006, but there were few breaking changes since then, and you won't run into them very often.

To be honest, I learned it using only the tutorial here: http://lua-users.org/wiki/LuaTutorial and google.