When troubleshooting a problem, many people overlook (or don't know) about a very helpful tool in the Utilities folder called Console. The Console is where programs often send warnings, errors, and information that the user doesn't necessarily need to see as pop-ups, but are still deemed important enough to save off. Sometime these messages are very technical; others are quite easy to understand.
When you start up the Console program, you'll seem messages that were sent by programs to the operating systems (which logs them in text files). Clicking on "Show Log List" in the upper-left corner will present a list of log files you can look at. If I'm looking for something happening right now, I will click on "All Messages", but if it happened in the past I may look up one of the more targeted log files.
You should see three major sections – "Database Searches", Diagnostic Information", and "Files". Database Searches looks through messages sent to the operating system (or just the Console Messages if you choose that). Diagnostic Information has crash logs, the same ones you might be sending off to Apple (in case you want to see them after they're sent or need to send the data again). Files lists the many log files on your system.
The list of files will depend on what software you've installed, as many programs will write their own logs. For example, if I open up /Library/Logs, I have logs for Adobe installers showing installation messages for many of the Adobe products I've installed. Usually, there's no reason to look at these, but if you are having an issue with an installation, this information could provide you or Adobe with reasons why something isn't working. Everyone should have ~/Library/Logs (these logs files are in your home directory), /Library/Logs (system-wide log files) and /private/var/logs, where Unix and other system information logs are. There are logs about software installations done with the Apple-written installed (/private/var/log/install.log) which is used by Apple and some third-party software. Under "cups" ("Common Unix Printing System") you'll find printing system logs, under "apache2" are the logs for your build-in web server (if you use web sharing), and so on.
You'll notice some logs have a number and ".gz" at the end. These are older logs that have been compressed to save space (but you can still view them). The daily, weekly, and monthly routines your Mac runs in the wee hours (if you don't shut it down) or as a catch-up later will archive these logs.
One of the ways to use these logs is to copy an error or warning message and search the web for it. Often times you'll find others with the same problem (and a solution) or you can just use these technique to learn more about what's going on.
Some of these logs can get large – if you're having an odd problem they can be very large indeed (I had a desktop machine that had a disk error – and decided to write about it until the disk filled up!). So you can use the Console to delete logs as well. Be care in doing this – if you aren't sure you should delete a log, don't! However, I have files under Adobe for CS3 installs, and since I have CS4, I'm pretty sure I don't need them. The same goes for other old files, such as crash reports (I've either already sent them on or I'm not going to after a day or so). Just select the log to delete and click on "Move to Trash" at the top (you can always get it back from the Trash if you made a mistake, but make sure you know where you got it from if you aren't on Snow Leopard, which lets you put stuff back automatically).