How to do I store photos on my airport time capsule without keeping them in my MacBook Air?

Basically you don't..

If you are using iPhoto apple specifically says not to store the library on network drives.

iPhoto: Issues with FAT32-formatted drives - Apple Support

Additionally, storing the iPhoto library on a network rather than locally on your computer can also lead to poor performance or data loss.

iPhoto: Sharing libraries among multiple users - Apple Support

So the answer is if you store an active live library on the TC you will eventually corrupt it.. don't do it.

The right way to share the library is on a Mac in your network.. or from iCloud. especially the new photo app in Yosemite is designed for iCloud.. it will give you issues on a TC.

Sorry.. Apple make this hard.

If your question is broader.. you are storing raw photos that is no problem.. copy and paste them.. but I suspect you are talking about iphoto or photos library rather than raw photos from your camera.

I am just replying to see if there is a comment.. the forum is working horribly at the moment and nothing is visible without new posts.