To look something up on the internet (world wide web). While the phrase "google" implies using mainly the google search engine, the phrase "webble" goes further by implying a broad-based search throughout the entire worldwide web for whatever information you happen to be seeking.
(1) I was looking for information on this new mp3 player I read about, but the guy at the store didn't know anything about it, so I webbled it. I found sites with user reviews and they all said it was actually a piece of junk.
(2) Kathy says to Bob, "Hey Bob, what is the weather supposed to be like this weekend?". Bob replies, "I don't know, let's webble it."