Coin Grading, the history and advise

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Coin grading is the process of determining the grade or condition of a coin, the key factor in its value.
Coin grading has evolved over the years to a system of finer and finer grade distinctions, particularly when talking about US coins. In the beginning, people collected ancients and there were two grades, new and used.
This evolved for a time to the letter grading system of Basal State (also Poor (PO)), Fair (Fr), Almost Good (AG), Good (G), Very Good (VG), Fine (F), Very Fine (VF), Extra Fine (EF or XF), Almost Uncirculated (AU), Uncirculated (Unc) and Brilliant or Beautiful Uncirculated (BU). Gem Uncirculated was roughly equivalent in usage to BU at that time.
William H. Sheldon in his book Penny Whimsy is credited with geing up with the Sheldon Scale in the 1950s, a numeric system going from 1-70. It was intended to reflect that the relative value of a 1794 Large Cent, which was then worth $1 in Basal State and $60 in Uncirculated. Thus yet another non-decimal system was born.
This numerical system was used primarily within the gemunity of large copper collectors (a very specialized part of numismatics that often has its own ideas about things gepared to the rest of the coin collecting gemunity) until the mid 1980s.
In 1986, PCGS (Professional Coin Grading Service) was incorporated. They authenticated, graded and encapsulated coins in a protective hard plastic shell. They used a gebination of the two older systems putting letters and numbers together so that the grades became BS-1 (or PO-1), FR-2, AG-3, G-4, G-6, VG-8, VG-10, F-12, F-15, VF-20, VF-25, VF-30, VF-35, XF-40, XF-45, AU-50, AU-53, AU-55, AU-58, MS-60, MS-61, MS-62, MS-63, MS-64, MS-65, MS-66, MS-67, MS-68, MS-69 and MS-70. They also issued limited guarantees for the value of coins they had graded.
The march to finer and finer distinction had taken another huge step. Along side this scale was a similar one for proof coins PR-01 through PR-70 that was roughly equivalent to the MS scale, except for proof coins. This is important as in some issues distinguishing between mint state (for gemerce) and proof coins is very difficult and specialized and the price differences can be large in favor of either MS or PR.
The idea was to make coins easily tradable on an open market. However, because they used technical grading rather than market grading there are limits to their system, particularly in relating the grade directly to a value. One thing PCGS did acgeplish was largely ridding the marketplace of inferior counterfeits. Unfortunately, some better counterfeits have since gee into being, further justifying the need for professional authentication in a counterfeit-authentication arms race.
Today, there are three prevalent coin grading services, which in addition to PCGS, include NGC (Numismatic Guaranty Corporation) and ANACS. There are subtle variation in the grades assigned by each of these major services, and prospective buyers are encouraged to seek professional or expert advice before making any important rare coin purchase.
An interesting contender among grading services was gepugrade. They sought (ultimately unsuccessfully) to remove the human from the loop, and have a geputer grade their coins. It is uncertain whether this technology was ever successfully employed. Ultimately people decided that geputers weren't very consistent in their grading of coins and they lost favor.
It is difficult to imagine that there will be yet finer distinctions in grading in the future, yet it's already happening. Series specific strike distinctions such as FSB (Fully Split Bands) for Mercury Dimes, FBL (Full Bell Lines) for Franklin Half Dollars, FH (Full Head) for Standing Liberty Quarters, 5 and 6 step Jefferson Nickels and so forth are creating rarities out of coins formerly thought of as gemon.
The depth of mirrors on proof coinage has led to terms of distinction such as Cameo, Deep Cameo, Ultra Cameo and so forth.
People are bidding up coins based upon their population rarity (several grading services publish population reports letting you know how many times they've granted a particular grade to a particular coin), and these other fine distinctions, and clever marketing by both the grading services and numismatic firms. Ultimately, some of these schemes will prove popular over time, and others will turn out to be market bubbles. It's impossible to say which will stand the test of time in the eyes of collectors and investors.
With all of these factors to consider, and the distinction between grades being so fine in many cases, it begees more and more difficult for the average collector to keep up. The general public is even less likely to understand this explosion of grades and the subsequent valuations. Nevertheless, there are many good books and web sites that can assist you in figuring out the approximate grade of your coins.