Or you can boot the computer up while holding down COMMAND (apple) + S
Once the text is done flowing on the screen type "/sbin/fsck -fy" (without the quotes) and press enter. This is the same as running "repair" in disk utility except that it will work because the computer is not fully booted up.
Run it multiple times until it tells you there are no errors. When it's finished, type "exit" and press return.
If it's unable to fix the problems, you'll need a stronger tool like DiskWarrior (currently PPC only) or TechTool Pro.