Before anything, you'll want to get yourself a digital drawing tablet (Wacom is pretty much the brand-of-choice, from my understanding. Though there may be some other more affordable off-brand tablets on the market, depending on your budget). It's pretty much impossible to draw anything decent with a mouse.
After that, Paint Tool Sai (if I recall correctly) offers a 1-month free trial, and it's a pretty solid piece of software (if I recall correctly, it costs around 40$). If you don't want to commit to anything that's going to cost money, GIMP is a pretty decent freeware program. Those two programs are what I started off with, and I think they're pretty good. (GIMP can be a little bit of a pain, though. Since it is freeware, it can be a bit glitchy at times.) By all means look up online tutorials regarding your program to help you get a hang of the ropes.
That being said, it is possible to make a web comic using traditional media, if traditional is your medium of choice. It is by no means required that you make webcomics digitally... To upload online, you just have to get yourself a scanner.
Best of luck!