At the most general level, a coin's grade is determined by how worn it is. Various numismatic agencies have gotten together and agreed on a specific set of "wear indicators" for each type of coin that can be used to determine where it falls on the grading scale. One example is the amount of the buffalo's horn that's still visible on an Indian Head nickel - none, half, full, etc.
At lower levels, say G up to XF, those criteria are about all you need. When you get into uncirculated and proof coins, things become a lot more specific (or picky, if you wish!) The grading committees look at things like how sharp the image is, whether there are any scratches from having been bagged at the mint, and other minute details.
Go to your local library and see if they have a copy of James Ruddy's Photograde book. It's considered to be one of the best general references, with pictures of many coins in different states of wear and how that relates to their grades.
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Each design has a different set of criteria. You can get a book such as Photograde that shows photos of many coins in different conditions in order to help match the ones you have to specific grading categories.
A Proof coin is a particular issue of a coin not a grade of condition.
The grade of a circulated coin is based oc how much wear it has.
Your grade will depend on the weight of the test in the overall grading scheme. If the test is a significant portion of your grade, it could potentially bring down your overall grade to a B or lower. However, if the test has less weight, your grade may still remain an A. To accurately determine your new grade, you would need to know the specific grading criteria for the class.
The term "Mint State" refers to the grade of a Uncirculated coin, The grading is not based on the amount of wear a coin has because there is none. It's based on how well the coin has been struck and the number an severity of any contact marks, scratches, rim nicks and scuff marks on the coin.