IIRC, Thawne starts off as kind of an obsessive Flash fanboy (who always had a violent streak). He gets plastic surgery to look like Barry Allen and then recreates Barry's accident (having researched the Flash a ton, he's already an expert on the Speed Force by this point) to become a speedster himself (which ages him considerably, so he actually looks like an older Barry). Then he finds and obtains the Cosmic Treadmill (damaged from years of disuse), and tries to use it to go back in time and meet his hero. Due to the Treadmill being out of shape, it misses the intended period, and he finds himself a couple of years after Barry's disappearance in Crisis on Infinite Earths, during Wally's tenure as the Flash. Thawne visits the Flash Museum (a common setting for many Flash stories, and which lasts long enough to have actually been a major part of Thawne's backstory in the 25th century), where he finds out he himself is destined to become Barry's archnemesis and to have his neck snapped by Barry (it later turns out this didn't kill him, as he returns from his Negative Speed Force around the same time Barry returns from inside his own Speed Force). This drives him somewhat mad, and he starts to become convinced he's actually Barry Allen, and he operates as the Flash for a short time along Wally West (who went back to a sidekick role for this period). I don't entirely remember what happens after that, but I think Wally realizes he's much more violent than the Barry he knows, and eventually Thawne gets sent back to his own time, where he starts using his powers to be a criminal. After a while he's gone full villain and, still obsessed with Barry, starts being Barry's archnemesis as "prophesied".

Of course not all of this happened when Reverse Flash first appeared, as he's a time traveler over the decades the blanks of his backstory have been slowly filled in. I'm not entirely sure where this fits in, but I think evil Thawne hates Barry for the whole necksnapping / Wally ordeals (there could be more to it though).