It Was a Dark and Stormy Day
Invent a Sentence Day could be difficult, depending on how well-read you are. You might come up with something you thought was unique, but when someone else reads it, they point out to you that it was already used in a Star Wars fan-fic (sp?) based on the early years of Hoth.
The sentence you create should make sense in English. You can't just string words together, capitalize the first one, put a period at the end, and call it a sentence. Good grammar and meaning must be present.
Your sentence should try hard to be strange enough that proving its uniqueness isn't something that even needs doing. Obviously, the Star Wars example above wasn't strange enough. Get weirder than that.
Once you've created something you think is suitable, you need to write it down in a place that others can see it. Just writing it on a piece of paper at home isn't good enough. That's like the sound of a tree falling in the forest...or something like that.
Obviously the most logical place to write it is online. You have your choice of places to put it there. The most logical, of course, is Reddit. If it's a question, Quora would work. If you're not signed up at those places and have no desire to do so, you could default to Facebook. Google+ is not an option because no one will read it there.