First, for newer collectors; coins are currently graded on a 70 point scale, often called the Sheldon scale because it was developed by DR. William H. Sheldon in 1949. Technically speaking, the current 70 point scale we used today is an adaptation of Sheldon's scale, and isn't exactly like his original.
There are two major sections in coin grading; Circulated coins, which are coins that have signs of wear, and Uncirculated coins, which show no signs of wear.
Now for the actual grades: Business Strike coins
*Sometimes different abbreviations are used, for instance PR and PO for poor, I have listed the abbreviations used by NGC and PCGS, in that order*
Poor 1- (PR-1, PO-1) This is the absolute lowest grade a coin can receive.
Fair 2- (FR-2, FA-2)
About Good 3- (AG-3)
Good 4 to Good 6- (G4, G6)
Very Good 8 to Very Good 10- (VG8, VG10)
Fine 12 to Fine 15- (F12, F15)
Very Fine 20, 25, 30, 35- (VF20, VF25, VF30, VF35)
Extra Fine 40 to Extra Fine 45- (XF40, XF45)
About Uncirculated 50, 55, 53, 58- (AU50, AU53, AU55, AU58) AU58 is the highest grade a circulated coin can receive
Mint State 60-70- (MS60, MS61, MS62, MS63, MS64, MS65, MS66, MS67, MS68, MS69, MS70) The lowest grade for an uncirculated coin is MS60, and the highest possible grade a coin can obtain is MS70.
Proof Coins: Proof coins are graded on the same scale as business strike coins (1-70). The only difference is the word proof is always used in the grade. What I mean by that is, a Proof coin that has light signs of wear wouldn't be called an AU58, it would be called a Proof58.
The abbreviation used by PCGS for Proof is PR, while NGC uses PF. So the most heavily circulated Proof coin will be a Proof 1 (PF1, PR1) and the highest grade will be a Proof 70 (PF70, PR70).
Once you have an understanding of the numeric grading system the next step is to apply that system to actual coin grading. The key to accurate coin grading is experience. There are a number of great sources out there that can help you build that experience. First, if your collecting U.S coins, there's The Official ANA Grading Standards for United States Coins a great book that will teach you the basics of U.S coin grading. Another way to build your grading experience is through coin pictures, one great source for coin pictures is Heritage (www.coins.ha.com), they take good pictures, and have a massive archive of past coin auctions. There you can compare and contrast coins of all grades, to get a good feel for how coins are graded.
The Star ✮
I'll start off with the NGC Star designation since it came first. NGC's Star Designation
The NGC star designation is given during the normal course of grading, if all 3 graders feel the coin deserves the star. As of January 1st 2008 all U.S coins except MS/PR 70 are eligible for the star. The star designation is all about eye appeal, it has nothing to do with the grade of the coin.
The NGC Star Designation identifies coins with exceptional eye appeal or characteristics that distinguish them from other coins of the same technical grade. This does not mean that they just miss the next grade, but it can mean that they verge on the next designation. For example, an untoned PF 65 Cameo coin is not necessarily close to the PF 66 grade, but may be close to an Ultra Cameo designation.
must have full vibrant luster, be free of any obvious planchet irregularities, and display no bothersome spots or blemishes.
The other way, that is explained above is if the coin is on the verge of the next designation (Don't confuse that with grade). The next designation can be PL, DMPL, Cameo, Ultra Cameo, so a coin that is on the borderline, but falls just short of one of those designations can also receive the star.
For example this is often seen in Morgans, where one side of the coin has PL or DMPL characteristics and the other side doesn't. This is a coin that could receive the star.
The Plus ✚
It's important to note that while PCGS was the first to announce, and use the plus designation, NGC is also going to start using the plus designation. The plus was announced on March 25 2010, as part of PCGS's "Big One", and it has everything to do with the grade of the coin. The plus designation is used to identify PQ (Premium Quality) coins. The plus designation is currently available for coins graded 45-68 excluding 60 and 61, and is only currently available through PCGS Secure Plus grading tier.
The way it works is like this: The coins entered under the secure plus tier are now graded on a 3 digit level, what that means, for instance instead of grading a coin MS65 a coin is graded MS654, or MS658 (anywhere between 0-9, MS651 being a low end 65, and MS659 being the highest 65). *That extra digit doesn't show up on the slab*, so each grader grades the coin on a 3 digit level, and a consensus is taken. It the coin is considered to be in the top percent (the .7-.9 level) it is given the + designation.
David Hall explains the + designation in detail in this video:
So the star is all about eye appeal, nothing to do with the grade. While the + recognizes PQ coins for the grade.