The key is you say you can use this with a PC. That means it is very likely the drive is formatted to NTFS which Macs can read but cannot write.
There are utilities such as NTFS-3G which can add capability, though they are not ideal. Likewise others to enable Mac formatting on PCs.
If the files are small ones you can re-format the drive (back up first!) and use FAT format which both computers can use.
Often the best thing is unless you absolutely have to use this drive with both computers just get another one for Mac use.
[10.4: An overview of NTFS support in Tiger|http://www.macosxhints.com/article.php?story=20050521110452194]
NTFS drivers for newer Macs (there may be others, and I am not sure if these will work with Tiger):
Paragon NTFS - http://www.paragon-software.com/home/ntfs-mac/ - recommendation: https://discussions.apple.com/thread/4046285?answerId=18708633022#18708633022
Tuxera NTFS 2012.3.2 - http://www.macupdate.com/app/mac/33122/tuxera-ntfs
NTFS for Mac OS X 9.5.3 - http://www.macupdate.com/app/mac/26288/ntfs-for-mac-os-x
Mac Drive for PCs - http://www.mediafour.com/products/macdrive