You're being downvoted I would guess because of the phrasing of the question ("install democracies" or "exporting democracy" are basically loaded phrases. To try to "install a democracy" has almost inherent connotations of a futile task, or even a euphemistic one at this point) but it is an interesting one, in the sense of "when did the United States start promoting democracy abroad?" And while I don't know enough about 19th century or turn of the century American foreign policy to answer that definitively I can say in answer to your question that it's been at least a century.

One of the more amusing primary source documents I've come across is this which are minutes of a meeting of the big four powers after World War I talking about how they are going to divide up the middle east: http://digicoll.library.wisc.edu/cgi-bin/FRUS/FRUS-idx?type=goto&id=FRUS.FRUS1919Parisv05&page=1&isize=L

The first several pages, presumably representing a significant length of conversation, consist of Britain and France squabbling over the extent of their commitments in the region, France for instance, noting that they had signed Sykes Picot, not Hussein-McMahon, in fact, had signed Sykes Picot without even being aware of Hussein-McMahon. Basically purely territorial disputes between empires.

Then Wilson pipes up about self determination and his desire to "establish the peace of the world." The result of all this was that the European powers placated the United States by allowing what would later be called the King-Crane Commission to be created. A commission designed to find out the wants and wishes of the Arabs themselves, because as Wilson said the wishes of Britain and France were immaterial "unless the peoples wanted them." i.e. unless they had something like a democracy asking for their presence. But it was basically a futile effort and Britain and France carried on with their imperial ambitions. Wilson himself brings up whether he was at the meeting as a right or as a courtesy, and carries on assuming it was his right. I think it's pretty clear from the record that he was there as a courtesy.