In short: You just need to create another partition, and make a filesystem on it. Then add it to /etc/fstab on both systems. Make sure your user IDs match. Add any bind mounts and/or symlinks you want for convenience.
Details:
First: this is much easier if your user ID numbers match on both distros. You can run id to check what your user ID number is. If they don't match, it'll be annoying (because there isn't a way to turn off permission checks on, e.g., ext4).
So if they don't match, you probably want to change one. The basic process is that you log out, log in as a different user, and use sudo groupmod -g new-gid your-group to change the group id and sudo usermod -u new-uid your-user to change your userid. At least on Debian, these are documented to also change ownership of your home directory and mail spool. You probably also want to do a find / -uid old-user-id -or -gid old-group-id to find any files or directories it missed and chown your-user:your-group filename to fix them. (I couldn't find a question to link to—so if you're at all unclear on this, please ask a second question, and link to this).
Second: You need a spare partition. Use your favorite partition table editor to create one. This presumes you have free space; if not, you'll have to shrink some existing partitions. I definitely recommend a backup before shrinking any partition. You'll probably have to reboot to activate the new partition table, go ahead and do so.
Third: format the new partition. E.g., sudo mkfs.ext4 /dev/sdaX.
Fourth: Create a directory where you want to mount it. You could put it in your home directory, but I think it'd actually be more useful to mount it somewhere else, then use bind mounts (for one thing, who wants a non-removable lost+found in his/her Documents folder?). You can put it wherever—hypothetically, let's say you mount it at /shared. You need to do this on both distros.
Add an entry to /etc/fstab on both distros. It should look something like this:
# dev mountdir fs options dump pass /dev/sdaX /shared ext4 defaults 0 2
Now, go ahead and mount it: sudo mount /shared. Create yourself a directory inside it (sudo mkdir /shared/your-username; sudo chown your-username: /shared/your-username).
You can now create subdirectories inside your directory (without sudo), and of course also files. You can also put symlinks from your home directory (on each distro)—e.g., if you've made a /shared/your-user/Documents, you could
# do these steps on each distro mv Documents Documents.old ln -s /shared/your-user/Documents Documents mv -i Documents.old/* Documents/ rmdir Documents.old
An alternative is to use bind mounts, but I'd not bother with that unless you really need them (e.g., to make a single directory read-only, etc.)