I basically owe nearly all my development to the internet sites that do their part to spread CM by their means (good or otherwise
) So I'll start off with a site with whom I've had a long history -- http://karnatik.com/ -- I prefer starting here : http://karnatik.com/infoindex.shtml
How did I find it? -- I ran into this long long ago in the last decade when searching for lyrics for some of the songs I was listening to and it's still one of those old runners that's still around.
What does it have? (It's not meant to summarize everything, maybe subsequent threads can). It's divided into these sections -- lyrics, references, fun stuff, a learning music section and a theory section. Among other things, these include :
1) A good introduction section with some helpful notes on the history of CM
2) Some good articles here : http://karnatik.com/articles.shtml
3) A good basics section : http://karnatik.com/beginner.shtml - covers the usual gamut - sarali, janta, dhattu, upper and lower octave verses, alankarams, geetams, nottuswarams, and finally the varnams -- the last 3 will take you to the pages where there are extensive lists of the items with lyrics for the same
Has useful guides where you can read the notation and how the verses are sung in 4 speeds and also listen to the basics too. There're some useful tips on how to practice too, identifying close ragas, a list of gamakas and other useful stuff.
4) By far the biggest contribution from this site is that it has an extensive song list (about 2400 compositions) of most well known compositions covering a huge range of composers and ragas. The list links to pages for the lyrics of nearly all the items on this list (and this is the site's greatest asset) -- occasionally you can get a translation too. For songs not on the list, you can mail (though I've realized since then it is Mr. Lakshman who provides the lyrics).
http://karnatik.com/lyricstext.shtml
You can also go to the composers pages and read some interesting info on their lives. You get lists of compositions sorted by composer and by raga too (which takes you to an EXTENSIVE A-Z listing of nearly 1000 ragas) -- all the links on these pages lead to the lyrics of the song.
Other interesting stuff - a huge list of film songs and the nearest equivalent carnatic ragas they were composed in, fun quizzes, a table of talas, Hindustani equivalent's to CM ragas, etc.. etc..., a melakartha list, even a jokes page...
I mainly used it for lyrics and that huge song list and (in the beginning) for some of the interesting references and fun stuff it had.
How to best use it : Online surfing. Or Google <a song name> lyrics. Chances are this will be on the first page. Or better, download the whole website
(http://www.httrack.com/)
once it has grown a little more) and I've been at it for years now. 
), but hey, I googled first and usually got anything I asked for.