I have seen instructions for resizing the partition here, but how do I create a whole new partition using the remaining space, and then mount it?
Type n to create a new partition.
Type p to make a primary partition.
Next press enter when prompted for a partition number to choose the next available.
Press enter again to pick the next available sector to start the partition. Press enter again to use all of the remaining disk space.
Type w to save the changes.
Fdisk will now exit. You am need to reboot in order for the partition to be available.
You can now make a file system for the new partition using the mkfs command.
Where x is the partition number.
Note: sometimes when creating a new partition for the sd card there has been a small amount of logical space that takes up the rest of the image. You'll need to use the method in the question you linked to in order to extend that space, or do as I do and just create another partition after it.
To mount you use the mount command like this:
mount /dev/sdax /path/to/mount/point
If you want the partition to mount automatically at boot then you need to add an entry in the /etc/fstab file.
/dev/sdax /path/to/mount defaults 1 0