The 1878 silver dollar is the Morgan Dollar. Uncirculated coins will have no wear on the at all. They may have scratches, nicks and scuffs but they will have no wear at all. Sometimes it is necessary to look at the coin through a magnifying lens to detect the slightest wear.
The national motto E PLURIBUS UNUM is on most all US coins dated 1878. If you are referring to a 1878 MORGAN dollar, the most basic thing is the weight and diameter of the coin. if you have doubts about the authenticity of the coin, take it to a coin dealer for an assessment.
An uncirculated coin has never been used in everyday commerce, it will have no wear.
Uncirculated means that the coin has never been used. So if it shows any wear, it can't be uncirculated.
A professional coin dealer or a professional coin grading service can determine if a coin is circulated or uncirculated. They will assess various characteristics of the coin, such as its condition, surface quality, and wear, to make this determination.
As far as I can tell there were no coins from 1839 with the E Pluribus Unum motto on them. Better re-check the date. Re-ask the question, giving more information about the coin, like what denomination it is, and anything else that is written on the coin.
"Uncirculated" means a coin has never been spent, and is in the same brand-new condition it was when it came from the mint. If your coin has any wear from being in change, it's no longer uncirculated.
You can't unless you pay the $20+ to send your coin to NGC/PCGs even under magnification the ordinary person cannot tell the difference between a pf69 and pf70 coin. Of course, it is easy to tell if your coin is uncirculated or proof, a proof silver eagle will have very shiny, mirror like fields that are easy to see yourself in. An uncirculated silver eagle will be shiny, but won't be mirror like. Also, the raised part of the coin will look frosted on a proof coin but not on an uncirculated coin.
We need more information before we can tell you. All coins say "e pluribus unum," so that is not a unique feature. Looking at some coin sellers, 1911 Liberty Head nickels range from $2 to $20. The value of a coin is not just about its year-- it has to do with how rare the coin is, how many were put into circulation, and what condition the coin is in.
It would have very little scratches or other dirt on the coin.
If the coin shows lots of wear, scratches, and dirt it is circulated. If it is still shiny, with very few scratches it will probably be uncirculated.
In the related links I have added links to the front and back of an uncirculated Barber quarter, yours should look the same if it is uncirculated (or possibly almost uncirculated) only with a different date. Keep in mind that if you want to sell your coin as uncirculated, you need to have it graded by a professional grading company before you will find buyers willing to pay a significant premium on it. Also, to the untrained eye, uncirculated and almost uncirculated coins look nearly identical, but a reputable coin dealer or grading company can tell the difference. And there is a huge price jump from an almost uncirculated coin to a mint state coin.
A uncirculated coin has no signs of wear and the coin should have full mint luster, but other things like contact marks and quality of strike may confuse a novice collector, take it to a dealer for an opinion.