I use Suse 9.0 installed on a hd in one partition (total of 1 gb or something like it). I started to run out of place specially on /usr. So I bought a new hd of 80 gb. That one I divided into 4 partitions with about 20 gb each.

My intention is to use them like this:
20 gb for use both in linux and win98 - formated and mounted without problem.

20 gb for making home larger
20 gb for making /usr/lib larger
20 gb for making /usr/share larger.

I used YAST2 to partition and format and mount the partitions like that but that made all data in the old /home, /usr/lib, /usr/share to disappear. Fortunately I managed to unmount them using the installation disk but now my question is:

How should I manage to use these disks without reinstalling the whole system?

I sounds like you need to copy the informion from you old partions, to the new ones. I'm guessing from your post that you current situation is that you are using you original hard drive without the new ones mounted, and that you second hd is hdb not hda. If my asssumtion is wrong please let me know.
To copy the data you will need to mount those drives in three seperate folders, as root. Here is an example of how to do this:

"mkdir /mnt/usr/share
mount /dev/hdb2 /mnt/usr/share"

Then copy /usr/share to /mnt/usr/share in konquerer.Then repeat this process for for the other two partions.After you finish copying do:

"umount /dev/hdb2
umount /dev/hda3
umount /dev/hdb4"

You can then go into YAST and set up the mountpoints like you had planned.

There are a few ways to do it. Taeuler's way should work. Let us know how it goes.

You can also do a mirror image of the partitions using partimage, or even from the command line to copy the partitions over. The important thing is to flag the mount points correctly, if you keep the drives jumpered as they are now.

I wanted to mention one thing. How old is the original drive? I also assume that the new drive is much faster than the old. It may be worth the effort (if the old drive is say more than 5 years old) to make your new drive your primary master. You could use the new drive's utility to format 20 gigs for Windows and copy your win installation to the new drive. If you decide to reinstall linux, then switch the jumpers on the hard drives so that the new drive is master and reinstall Linux (unless of course you have a lot of time invested in the Linux system).

Or, if you want to keep the current linux installation, you can set up windows, as described above, set up the partitions for linux, copy (mirror) the current linux data to the new drive and then switch the jumpers on the drives. The new faster drive is now your master primary and boot drive.

It depends on how daring you are. What I am getting at is the age of the old drive and the possibility of drive failure, if it is an old aging drive.