How do I move my iPhoto library to an external drive available through Time Capsule?
Couple of things: 


What format is the external?  iPhoto needs to have the Library sitting on disk formatted Mac OS Extended (Journaled). Users with the Library sitting on disks otherwise formatted regularly report issues including, but not limited to, importing, saving edits and sharing the photos.
Is that a wireless connection to the disk?  A strong warning: If you're trying to edit the Library (that is, make albums, move photos around, keyword, make books or slideshows etc.) or edit individual photos in it via Wireless be very careful. Dropouts are a common fact of wireless networking, and should one occur while the app is writing to the database then your Library will be damaged. Simply, I would not do this with my Libraries.