Everything you need to know about the API (which was changed a lot, and for good, with OS 3.2), is here :
http://wiki.inspired-lua.org It covers most of the essential API (although the latest things aren't fully documented yet), with syntax, descirption, examples...
It's based off the official API documentation by TI (
http://education.ti.com/nspire/scripting-api ).
Some theory and practice tutorials are available on
www.inspired-lua.org , however Steve Arnold has created a very well done set of tutorials, that go from beginner to advanced level, here :
http://compasstech.com.au/TNS_Authoring/Scripting/index.html .
The "best" way to code in the Nspire-Lua language is probably to get the Nspire Computer Software 3.2 which has its integrated Nspire-Lua SDK. You can create 3.1-compatible scripts within that 3.2 software, btw. (creating a document with only a lua script, and putting ' platform.apilevel = "1.0" ' at the beginning of the script.)
I however presented new ways to code with alternative editors during my T^3 speech, which you can find here (powerpoint and/or PDF) :
http://adriweb.free.fr/t3/ (the docs are also about improving one's lua skills by optimizations). A more beginner-friendly doc about improving one's skill in Nspire Lua can be found here :
http://tiplanet.org/forum/archives_voir.php?id=6720
There are several ways to code on-calc, the main one being the tool made by Extended : OcLua
I believe that if you have some Nspire-Lua oriented questions, you can post on TI-Planet (don't worry about English), since we do a lot of that there, and we'll be glad to help