The term "circulated" in the world of coins means not in mint condition. In particular, any coin that you find in change is by definition circulated.
The way you can tell is by looking closely at the coin and checking for dents, scratches, wear and other signs that the coin has been used (circulated).
If in doubt, get it graded by your local coin shop and have them evaluate it for you.
Circulated means used, so if it has any wear, it's circulated.
The grade of a circulated coin is based oc how much wear it has.
The most circulated coin would be the half dollar. I am not much of a coin expert but I have seen the half dollar mostly circulated then any other coin. That is if your thinking about coins that the mint had stopped making or don't make much of any more.
If you mean a $2.50 Gold coin dated 1908 retail values for a circulated coin are $185.00-$250.00 with uncirculated at $350.00+
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.
Assuming the coin is circulated and has no mintmark, the 1908 Barber dime is a very common coin, for a coin in average circulated condition the values are $2.00-$8.00 retail.
A coin which has "circulated" shows evidence of use in commerce, such as luster interruption, wear, circulation marks, dirt, etc. Conversely, an "uncirculated" coin displays no such evidence.
No mint mark10 to 75 cents for a circulated coin, $1.25 to $31 uncirculatedD mint mark10 cents to $1 for a circulated coin, $4.50 to $35 uncirculatedS mint mark12 cents to $1.75 for a circulated coin, $4.50 to $27 uncirculated
The difference is, a circulated coin has been used. An uncirculated coin has not been used and shows no signs of wear.
No mint mark10 to 75 cents for a circulated coin, $1.25 to $31 uncirculatedD mint mark10 cents to $1 for a circulated coin, $4.50 to $35 uncirculatedS mint mark12 cents to $1.75 for a circulated coin, $4.50 to $27 uncirculated
A uncirculated coin has not been used so it will not have any wear (or dirt) at all. You can also go on-line and find one of the many coin grading sites.
Any coin can be circulated or uncirculated depending on whether it's been spent in change or not. A coin that's received directly from the Mint, or from a bank that received it from the Mint without handing it out in change, is uncirculated. As soon as the coin has been spent, it becomes circulated. An analogy is buying a new car. The moment you drive it off the lot after paying for it, it's now a used car even if you haven't driven halfway around the block. Note: Unless you know a coin's "provenance" (a fancy term that means "where it came from") that's difficult to determine circulated versus uncirculated when a coin shows no obvious wear.