Why November 4?:

Why are elections held on the first Tuesday following the first Monday in November -- this year, November 4th?

A Congressional Research Service Report from 2001 provides the answer:
Elections for all federal elected officials are held on the Tuesday after the first Monday in November in even-numbered years . . . ; presidential elections are held in every year divisible by four. Congress selected this day in 1845 (5 Stat. 721); previously, states held elections on different days between September and November, a practice that sometimes led to multiple voting across state lines, and other fraudulent practices.

By tradition, November was chosen because the harvest was in, and farmers were able to take the time needed to vote. Tuesday was selected because it gave a full day's travel between Sunday, which was widely observed as a strict day of rest, and election day. [Footnote: In most rural areas, the only polling place was at the county seat, frequently a journey of many miles on foot or horseback.] Travel was also easier throughout the north during November, before winter had set in.

Some sources also suggest that Tuesday was picked over Wednesday because Wednesday was usually market day.
h/t: Volokh

Then there's Why Tuesday? is a non-partisan, nonprofit 501(c)(3) organization founded in 2005 to find solutions to increase voter turnout and participation in elections.