Welcome to FT! Some of the fare codes are standard in the industry: F = Unrestricted first class; C = business class; Y = unrestricted coach. Then there are a bunch of coach bases which have restrictions such as M, B, H, Q, V, W, T, etc. Generally the closer the letter is to Y (not alphabetically but in the UA expert mode listing), the lower the restictions but the higher the likely fare.
The numbers next to the codes (F8, C9, Y9, M3, etc.) indicate how many reservations are left in each fare class. There may be more than 9 fares left per class (if the plane is big enough) - 9 is the most that will show. Because all airlines, incl. UA overbook, this does not always correlate to how many "seats" are left. [Edited to add last par.]
If you get a fare quote on ual.com, placing the mouse over the "fare rules" will display the actual fare basis at the bottom of your screen, such as VXE7NR. This means a "V" class restricted coach discount fare that must be purchased at least 7 days in advance and is non-refundable.

[This message has been edited by Ocn Vw 1K (edited 07-11-2002).]