For a bill, it is comparatively easy. It should have no fold marks and the bill should feel "crisp" there should also be no tears in the bill.
For coins, you have to look at the wear, nothing should be smoothed down (although, particularly with earlier coin there are coins with weak strikes which looks like wear to the untrained eye) the coin might have scratches from being in a bag with other coins (although these do decrease the value, they are not considered wear and the coin will still be considered uncirculated with scratches) different coins have different high points where wear first starts to show, often on coins bearing a side view of a portrait, the wear will start at the ear.
An uncirculated coin has never been used in everyday commerce, it will have no wear.
The term "Uncirculated" means any coin that has not been put into circulation.
An official "US Mint Set" is a Uncirculated coin set. They have uncirculated examples of every denomination issued from each mint for the year of issue. They are the same.
almost uncirculated
If the coin is uncirculated the retail value is about $4.25 if it's not, bullion value is $3.00 as of today.
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.
"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.
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.
A uncirculated coin has no wear at all, but may have contact marks.
My father is an antique and coin auctioneer and gets between $5 and $10 per bill when they are sequenced and 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.
An Uncirculated $2.50 gold US coin is worth $425 in MS-60 uncirculated.
Not really. While I suppose it is possible for one side of a coin to be uncirculated while the other side is only almost uncirculated, a coin couldn't be both brilliant uncirculated while being almost uncirculated.
A Mint issued uncirculated coin set has a current value of $8.00.