Were duels normal in early American History?

by -the-correct-answer-

How did people think about them? When would they appropriately come up?

Georgy_K_Zhukov

Duels were very rare in colonial America, if that is what you mean by 'early'. There were a few, here and there, but they were rare, and it was rarer still that it was fought between two colonists, with most of them involving military officers and recent arrivals from England as members of the colonial governments. The best known exception was the 1728 Philips-Woodbridge Duel, which also helps to illustrate the harsh views on dueling in colonial America, with Philips fleeing the continent for France to escape a murder indictment from the colonial Massachusetts government.

Dueling really starts to take off in the US during the revolutionary period, in large part helped along by the war itself. American officers adopted the practice in imitation of their French and English counterparts. After the war, the institution stayed. For a time it was practiced in northern states with strong political overtures, but following Hamilton's death, there was a marked decline. In the South however, it became quite ingrained into the elite planter culture's values, and continued through the 1860s. I apologize for the slight brevity here, but I've written several other pieces on this which expand further, and can be found here. The Hamilton AMA especially is right on point for this.

I'd also recommend as further reading “The Code of Honor in Colonial and Revolutionary Times with Special Reference to New England.” from Publications of the Colonial Society of Massachusetts 26 (1927) by Evarts B. Greene, and "Affairs of Honor: National Politics in the New Republic" by Joanne B. Freeman.