If you want the easy GUI way, try pysdm. Install and then run it, like this:
sudo apt-get install pysdm
You will see the available partitions in the left pane something like sda, stb, ... You can click on them to reveal the logical partitions there. Choose the one that looks like the old partition. It is likely to have the type "ext4".
Assistant to change the options as desired, for example, to enable auto-mount on boot. Or enable read-only mode should you want to protect the mounted partition.
You should also specify the "Mountpoint" as the directory where you will be accessing the mounted partition. Something like /media/oldstuff might do. You may choose an existing (empty) directory, or create a new one.
Then click on
Mount. The partition should be mounted now.
How it works: The program edits the /etc/fstab file where the mounted partitions are defined. An expert might edit the file directly. You might want to make a backup copy before trying. And if you want to do the mounting by hand - read