Your rank in the contest depends primarily on how many problems you solve (column Slv. on the standings page) and in case of ties on the total time it took you to solve the problems (column Time on the standings page), and as a final tie-breaker on when you submit your last accepted solution.
You have solved a problem if you have submitted a program (before the end of the contest) that was accepted by the judging system. If contestant A has solved more problems than contestant B, then contestant A has a lower rank (places better) than contestant B. The winner is thus the contestant with rank one.
If two contestants have solved the same number of problems, then the one with the smaller total time has lower rank (places better). The total time is defined as the sum of the submission times of your accepted submissions (don't worry, there will be an example) and any penalty time for incorrect submissions. Only the submissions you have made to problems you solve contribute to your total time. Penalty time is computed as follows. You get 20 minutes of penalty time for each incorrect submission you make to a problem prior to solving it. Penalty is given for the judgements Wrong Answer, Run Time Error and Time Limit Exceeded (see possible judgements).
Say a contestant has
The contestant has solved two problems. Since problem B was not solved, those incorrect submissions do not contribute to the total time. Problem A contributes 30 + 2*20 minutes to the total time, and problem C contributes 45 + 1*20 minutes. This gives us a total of 135 minutes. For the purpose of computing total time, the time of submission is rounded down to the nearest minute.
The final tie breaker, in case two contestants solved the same number of problems and have the same total time, is the time of the last accepted submission. In other words, if A and B both solve 5 problems, and they both have total time 674, but A submitted her fifth accepted solution before B, then A gets a lower rank than B (that is, A places better than B).
Two of the judgements that lead to rejection of your submission (see possible judgements) do NOT result in 20 minutes penalty time: Compile Error and Judge Error.
On the standings page cells are green, red, gray or white.
The first number in a cell is the number of submissions you have made on that problem. For an accepted submission (green cell) the second number is how many minutes into the contest you made the accepted submission.
During the last hour of the contest the result of pending submissions are not revealed. That is, gray cells will not turn either green or red. You will still get the results for your own submissions, but you cannot see on the standings page how submissions made during the last hour are judged.