I have heard that Hitler was democratically elected, however time and time again I hear things to the contrary of that statement. What is the truth?
The situation is complicated by the executive structure of the Weimar Republic. The Weimar constitution held that the President would appoint a Chancellor that would then run the cabinet and coordinate with the Reichstag. So technically, when Hindenburg tapped Hitler to the Chancellorship in 1933, he was not elected, but appointed. But this system of appointment does not make the Weimar executive system undemocratic. A number of parliamentary liberal democracies such as Germany today, the UK, Japan, have a system in which an individual is designated as the executive through an inner-government vote rather than from the people. One of the Achilles' heels of Weimar democracy was the mechanism for election to the Chancellery relied on a very narrow circle. Hitler's appointment was in the bounds of the existing German constitution and was legal; he was the leader of the largest party in the Reichstag and Hindenburg did not really violate the terms of his office in appointing Hitler.
All of this though is irrelevant. Hitler may have used democratic means to vault into power in 1933, but he had no intention of governing democratically. The Enabling Act passed by the rump Reichstag was just a capstone to a series of measures designed to tear the guts out of German democratic systems in the hectic weeks following Hitler's appointment. The Weimar system may have been democratic, but it had very little mechanisms to prevent someone from actively sabotaging it.
Also, upon the passing of the President in the summer of 1934, Hitler appointed himself President. That violated the terms of the Enabling Act of 1933, which expressly forbade the Chancellor modifying the institution of the Presidency. He then held a referendum to approve his seizure of the office. There was a real campaign and vote but, of course, it wasn't an open and democratic election by any means as the ballots were probably not secret in most places. Hitler carried 80% or so of the vote. Some historians say it is remarkable how unified the Germans were in supporting Hitler's move. Others say it is remarkable, on the contrary, how many were brave enough to defy him. I lean slightly towards the latter. Most people by this point were familiar enough with Nazi methods to understand the risks they ran. The fact that anyone showed up to vote no is pretty amazing.