When Han Solo tells Finn and Rey that Luke Skywalker, The Jedi, and The Force are all true, Rey does not respond, "Yah, I know." She instead gazes in wonder at the magical possibilities. How then could this industrial picker, isolated on a desert planet her entire life, shortly thereafter not only conceive of the notion, but then earnestly attempt to telepathically persuade a stormtrooper into releasing her from captivity, especially since Han Solo did not offer any particulars? This is my theory.
It is important to note this exchange between Solo, Finn, and Rey happens before Kylo Ren attempts the Mind Meld on Rey to extract the missing piece of the map. It is during this psychic struggle that I believe Rey acquires the knowledge of The Force's and her own (heretofore dormant) Force-capable potential. It is Kylo Ren's incomplete tutelage under Skywalker that permits Rey a glance at this potential. It is Kylo's lack of mastery over this technique that provides Rey the knowing of things that we don't grant she can know.
If Kylo's training had been successfully completed, he likely would not have been sloppy enough to spill The Force's beans, to subconsciously reveal to Rey that she has tools like the Jedi Mind Trick and telekinesis at her disposal.
UPDATE: Sonny Bunch was kind enough to consider the possibility of this theory.
@obamuh Possible!— Sonny Bunch (@SonnyBunch) December 22, 2015
Editor's Note: Thanks, Sonny!