you are having a couple of options
1) delete the unnecessary log files form var partation ( var is the partation, which holds the log messages generated my most of the system services)
2) if you want to automate the process of deleting the old log files, use the logrotate tool, which is availabel under linux.
3) if you want to add space to existing var partation, check the following options first
a) if you partationed teh var as a separate partation, then you can use the LVM ( Logical Volume Manager). it is similar to volume mamagment softwares available under windows 2000. it is like adding multipul volumes to make a chian. but you need to add extra hard disk or use any existign empty volumes.
Cheers