I make charts of songs that are good candidates, good targets, so to speak. Then I try to come up with ideas for parodies. And 99% of those ideas are horrible.
It's hard to really articulate what the parameters are that make one song parody-able and another song not, but if I can come up with a good enough idea for it, I go for it, and if not, then I have to move on.
In fact, when I come up with an idea for a parody I try to resist the urge to Google the idea to see if someone has done it already because the answer is almost always, "Yes, of course they have, they've thought of it!"
I start with a comprehensive list of all the recent songs that have been big hits - and then I go down that list and see if I can come up with funny ideas for them. I can always come up with ideas, but not necessarily good ones!
My process for the parodies is that I get an idea for a song and then get approval from the artist and then go in and record it and probably try to get it out as soon as possible.