Zeebra, I don't believe lud is fully correct. Parties can choose and reject their candidates in any way they see fit. However, anyone can run for office if they meet some minimal requirements. As previously stated some states require that presidential candidates gain so many citizen signatures before they will be typed on a ballot, otherwise the list would be pages long and impractical. However, any candidate can be written-in in the provided blank spot. That means I could vote for myself and others could too if I met the requirements.
The difference between Iran and the US is that there is no subjectivity to the US election process. The people vote and whoever has the most electoral votes wins, period. Our country has a two party system, not because its mandated but because the majority of americans agree the most with one or the other party. Overnight this could change and we could have 0, 1 or any number of viable parties. It all depends on how the people choose. No one is forced to vote for a particular party. Just because it happens that a two party system has evolved doesn't somehow mean its no longer a democracy.
Iran is not a democracy. The people vote but their vote is worthless because nothing gurantees that the elected person will get in. Moreover, elected officials are still subserviant to the mullahs. For example, if 100% of the country voted for adjimihad then he isn't guranteed to get appointed because a small group of people decide, not the voters. The people have ZERO say. They just get to say who they would PREFER but the gov't is under no obligation to oblige. This is unlike the US where if a person, no matter what party or affiliation, receives a majority of electoral votes then he will be the new president. Neither the SCOTUS or congress can change this.
Now if you wanted to point out how america isn't a democracy then you would have some valid points if you discussed the electoral voting system. This is why the US is actually a constitutional republic. But, as others have said repeatedly, the term "liberal democracy" as used by the US and other western countries isn't defined by voting alone.
You've got a lot more to learn. This barely scratches the surface.