Nearly all of the flash artists on NewGrounds use Adobe Flash. You can get the free trial there or buy the full thing. However, Flash is pretty expensive so you might be interested in some alternatives. First off is the student version of flash(NB: You have to be student in the USA or Canada for this and you can not make profit off your works). You can also buy older or used versions of flash for alot cheaper than the huge $700. You might be able to find some of these by searching: Macromedia Flash Or Adobe Flash.
There are not only adobe programs. There are also some cheaper, but not as good, versions out there. Heres a list:
SWiSH Max - $100 (Free Trial)
ToonBoom - $399 (Free Trial)
LiveSWF - Free
KoolMoves - $59 (Free Trial)
SoThink - $85 (Free Trial)
Anime Studio - $49(Pro - $179) (Free Trial)
Once you've got yourself a program head over to the flash tutorial section and start learning flash. Other learning resources for flash include:
Kirupa
FlashWiki
actionscript.org
gotoAndLearn
AS dictionary
AS: Main
Tutorial Collab '06