To draw your average Pasta Disaster I use a Wacom Volito 2 drawing tablet and this cheap and cheerful photo editing software called PhotoImpact 6 by Ulead.
I also keep a notepad doc in my folder labeled 'ideas' which I add to whenever I think of a catchy one-liner that could be turned into a cutesy 515 x 499 pixel image.
Some Pasta Disasters are completely hand drawn, others rely on a sort of naive vector art. At least, I think that's what you could call it. I normally draw a few in a day and use them as a buffer so I can upload regularly and people will think I'm consistently creative. What they don't know can't hurt them.
On occasion a PD could be a scanned image manipulated somewhat and then cropped to size. I've also been known to just post a photo. One time I wrote a poem. This is just my space to be as strange as I dare.
I hope that has been educational. Now, hurry up and try the noodles!