One thing to be aware of is that, in the aftermath of the American Revolution, the United States was entering into uncharted territory. There were no examples in Europe of republicanism practiced on the kind of geographic scale of the United States, so to a large degree, democracy in this country was a work in progress.
Indeed, it should be noted, the United States has actually had two separate founding documents. Originally, it was organized under the Articles of Confederation, which envisioned a very decentralized balance between federal and state power, but in practice, this original political structure proved unable to answer the challenges of the post–Revolutionary War period. With this in mind, the Constitution was drawn up to replace it and provide a new approach to organizing large-scale democratic government.
However, even so, many critical United States government traditions would only arise in the process of actually running a United States government. So it was with the Presidential Cabinet, or the two-term limit, precedents which were set by George Washington himself rather than enshrined in the original US Constitution. Political parties likewise emerged organically, originating in a political struggle between Alexander Hamilton and Thomas Jefferson. Hamilton and his followers formed the Federalist Party and Jefferson's side formed the Democratic-Republican Party. Political parties have been with us ever since. Your question on elections fits into this same theme: to take presidential elections as an example, the Constitution originally stated that when compiling the votes, the person with the highest tally would become president and the person with the second highest vice president. However, in practice, this proved unfeasible, especially in a world of political parties, and with the Twelfth Amendment, it was changed so that president and vice president would share one ballot. The methods and tactics of campaigning would likewise evolve over time, as political candidates would find better and more effective means of mobilizing support to get elected.