Lots of articles out there that have almost the right solution here but nearly all of them miss one critical component, so for my future sanity, here’s what works for me:

sudo mount.cifs //timecapsule.local/Data/ /mnt/directory/ -o “pass=password,sec=ntlm”

If you don’t have zeroconf working in your Linux install you’ll have to use the time capsule’s IP instead of it’s .local name.  The “Data” part is the name of the disk you want to mount as shown in Airport Utility (make sure you escape any spaces with backslash.

Critically, you need to insist on NTLM authentication using the sec=ntlm option.  You may additionally want to specify file_mode, dir_mode and other standard mount options.

If you are using disk or device password based security you only need to specify the password, the username is ignored. However, if you’re using account based security you’ll need to also supply a user= option to specify the correct username.