Write audit logs for program startup, session startup, and for suspicious activity. Possible information of value includes date, time, uid, euid, gid, egid, terminal information, process id, and command line values. You may find the function syslog(3) helpful for implementing audit logs. One awkward problem is that any logging system should be able to record a lot of information (since this information could be very helpful), yet if the information isn't handled carefully the information itself could be used to create an attack. After all, the attacker controls some of the input being sent to the program. When recording data sent by a possible attacker, identify a list of ``expected'' characters and escape any ``unexpected'' characters so that the log isn't corrupted. Not doing this can be a real problem; users may include characters such as control characters (especially NIL or end-of-line) that can cause real problems. For example, if an attacker embeds a newline, they can then forge log entries by following the newline with the desired log entry. Sadly, there doesn't seem to be a standard convention for escaping these characters. I'm partial to the URL escaping mechanism (%hh where hh is the hexadecimal value of the escaped byte) but there are others including the C convention (\ooo for the octal value and \X where X is a special symbol, e.g., \n for newline). There's also the caret-system (^I is control-I), though that doesn't handle byte values over 127 gracefully.
There is the danger that a user could create a denial-of-service attack (or at least stop auditing) by performing a very large number of events that cut an audit record until the system runs out of resources to store the records. One approach to counter to this threat is to rate-limit audit record recording; intentionally slow down the response rate if ``too many'' audit records are being cut. You could try to slow the response rate only to the suspected attacker, but in many situations a single attacker can masquerade as potentially many users.
Selecting what is ``suspicious activity'' is, of course, dependent on what the program does and its anticipated use. Any input that fails the filtering checks discussed earlier is certainly a candidate (e.g., containing NIL). Inputs that could not result from normal use should probably be logged, e.g., a CGI program where certain required fields are missing in suspicious ways. Any input with phrases like /etc/passwd or /etc/shadow or the like is very suspicious in many cases. Similarly, trying to access Windows ``registry'' files or .pwl files is very suspicious.
Do not record passwords in an audit record. Often people accidentally enter passwords for a different system, so recording a password may allow a system administrator to break into a different computer outside the administrator's domain.