Oh boy I'm gonna try really, really hard not to violate the policies of this site.
I have studied extensively the cursing of the Civil War because I am working on a script set during this period and want my characters to curse accurately. I do my best to draw cursing not from lists of expressions but from the actual letters and diaries - it is not enough to simply know what words were used, but how they were used and when.
What I have gathered is that cursing was conducted in much the same manner as it is today, just with a few slight variations.
"F***" was only used to mean intercourse. It was not used as an intensifier or as an insult until around the First World War. Humorously, during the First World War it was said that if an officer shouted, "Grab your f***ing rifle and get the f*** over here" there was nothing to worry about, but if they said, "grab your rifle and get over here" you were probably about be overrun.
"Sh*t" was in use to mean excrement and the act of defecating and it seems also to have been used as an expression of anger or frustration (but I'm not positive about that). "Pinch of sh*t" was also used as an expression, as in, "your opinion ain't worth a pinch of sh*t."
"D***" and all of its derivatives were the most commonly used swears. It was much more intense at the time given the religious connotations. It was often seen in the form "God d***ed" or just "d***ed."
"Bas***d" did not come up nearly as often as I thought it would. In fact, it seems to have not come up at all. Perhaps it was still too closely tied to "being born out of wedlock" to be just a general insult.
Instead of saying, "kiss my a**" as we would say today I saw far more instances of "suck my a**" which I got quite the kick out of. Also instances of "a**" alone being used as an insult.
Where Civil War soldiers really had fun was with variations of "son of a...." and prostitution. While the common "son of a b***" was used I found they more often would say "son of a wh*re" (am I allowed to type wh*re?).
I think my favorite use of that pops up in the novel Play for a Kingdom which does an excellent job accurately recreating Civil War speech. One character says to another one, "Get bug***ed, ye who*rehouse p*mp," which is an absolutely correct period swear.
"C***" was used to refer to male genitalia, although not nearly as much as Showtime would have us believe. "P***" was also used to refer to urine and "p***ing" to the act itself.
Many threats to "spread your guts across the parade ground" are also found in court martial records.
Surprisingly, "shut up" was in use as an expression at the time.
And, obviously though unfortunately, "n*****" was often used to refer to African-Americans. Comparing someone to a "n*******" could be a pretty harsh insult.
This is just what I remember off the top of my head - I can't remember where I saved my word document explaining it more thoroughly.
And this isn't even to begin to mention the dirty language associated with intercourse, or as the soldiers sometimes called it, "horizontal refreshments."
And as always, when reading these I'm sure you'll find that you can, in the words of the late, great Terry Pratchett, "effortlessly pronounc[e] a row of dashes."
I sincerely hope I did not violate any of the policies of the site in this post....