[M] Modified Median
Of the two median tiebreaks, Modified Median is the more standard now. It evaluates the strength of a player's opposition by summing the final scores of his or her opponents and then discarding either the highest of these scores, the lowest, or both, depending on the tied player's score.
For players who tie with even scores (that is, their number of wins and losses is the same), both high and low are discarded. For tied players with plus scores, only the lowest is discarded, and for players with minus scores only the highest is discarded.
For tournaments of nine or more rounds, the top two scores are discarded (or the bottom two scores, or all four, as determined by the same even/plus/minus criteria above).
These scores are adjusted for any unplayed games, which count a half point each. If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0,
[S] Solkoff
Solkoff is just like the Basic Median except that no opponents' scores are discarded. Popular with tournaments of only a few rounds.
[B] Basic Median (Harkness Median)
Basic Median works just like the modified median above, but highs and lows are discarded regardless of the tied player's score. Generally the modified median is preferred to this nowadays.
[C] Cumulative Score
Cumulative Score is easy to calculate by hand, and has been popular for that reason. To get this value just add up the cumulative (running) score for each round. The theory is that players who win their games in the early rounds (and therefore end up with higher cumulative scores than players with the same score who win later rounds) have had to face tougher opposition throughout the tournament.
[P] Performance of Opposition
This method averages the performance ratings of the player's opposition. A player's performance rating is calculated by crediting the player with the opponent's rating plus 400 points for wins, minus 400 points for losses, and the opponent's rating for draws.