To give a reasonably indication of a players current strength the grading system tries to even out short term fluctuations caused by players playing only a few games during a season. With each grade in the list a letter is given indicating how many seasons the grade is calculated over. For the grade to be taken over just one season at least 30 games need to have reached the grader. For all grades every game in the preceding season is included in the calculated grade.
The letters are explained as follows:-
A  The grade is based upon 30 or more games in 2003/4
B   Based upon 30 games in 2003/4 and 2002/3 of which at least 20 were played in the current year.
C   Based upon 30 games in 2003/4, 2002/3 and 2001/2 of which at least 10 were played in the current year.
D  Based upon 15 or more games in 2003/4, 2002/3 and 2001/2 of which at least 5 were played in the current year.
E   Based upon 10 or more games in 2003/4, 2002/3 and 2001/2 of which at least 1 was played in the current year.
*   An asterisk means none of this criteria were satisfied.

Each grade is based on the average opponents grade with a 50 point bonus for wins and a 50 point deduction for loses. So for a player playing 38 games during the 2003-2004 season, with an average opponents grade of 156 and scoring 15 wins, 10 draws and 13 loses their grade is calculated as follows::
38*156 + 15*50 - 13*50 = 6028 grading points, this is then divided by the total number of games, giving 6028/38 = 158.63, this is rounded to 159.
A simple way of estimating your grade is as to work out the percentage score, and to estimate the average grade of opponent. So for the previous player who scored 100*(15+10/2)/38=52.63%, which is +2.63% above average, the grade is then 156+2.63=158.63.

A second example of a player with the following record would have a grade taken over 3 seasons and end up with a grade of 134C
2003-2004 season 12 games with an average opponents grade of 130 scoring 4 wins, 3 draws and 5 loses
2002-2003 season 15 games with an average opponents grade of 134 scoring 7 wins, 2 draws and 6 loses
2001-2002 season 13 games with an average opponents grade of 138 scoring 6 wins, 3 draws and 4 loses
From the 2003-2004 season the player has (130*12)-50=1510 grading points.
From the 2002-2003 season the player has (134*15)+50=2060 grading points.
From the 2001-2002 season the player has (138*13)-100=1894*(3/13)=437 grading points.
Note from the 2001-2002 season the player needs only 3 games to make up the quota of 30, so only 3/13ths of the seasons points are used.
Adding these together (1510+2060+437)/30=4007/30=133.57, this is rounded to the nearest integer to give a 134 grade.

For more detail look at how the BCF explain the grading system