If you have windows XP you will usually find you Signatures under
C:\Documents and Settings\
If your login name is Linda under XP then usually the
C:\Documents and Settings\Linda\Application Data\Microsoft\Signatures\
You can always do a search of your system to find the location of your signatures as well.
Once you find where your signatures are you can copy them to your new station or on a USB drive to transfer. Copy everything out of the \Signatures directory and place it back into the directory on your new drive which will be something like this:
If you can't see the AppData directory you probably need to change your folder and view options. All Windows operating systems hide by default system folders. You will need to click on your computer and bring up File Explorer and go to Folder and Search Options in Windows 7. Then click the View tab. Click on "Show hidden files, folder, and drives". Save by clicking OK. You will now be able to browse to the above locations.