You don't mention if the drive is currently mounted or not, but as long as it's possible to mount the drive, you should be able to access your files, at least for a short while assuming the drive doesn't completely die. In other words, if you can mount it, you'd want to mentally rank your important files, and start copying the most important first.
Assuming that the directory /mnt/hd exists, you would manually mount this partition (as root)
mount /dev/hdg1 /mnt/hd
If it works, the contents of the crashed drive should appear under /mnt/hd, and from there you should be able to copy them to a safe place. (If /mnt/hd does not already exist, you can create it by running "mkdir /mnt/hd" (no quotes)
Good luck with it, crashed drives are an iffy propositiion at best. If the data is really valuable, there are professional data recovery services available, but they can charge several hundred dollars per hour for their work, and it may not be worth the money. -- J.W.