How can I add a photo to a contact? It seems like this should be possible - how can I add a profile photo to a contact that I manually created? At the moment they're all boring silhouettes.

In my Contacts, the only ones with photos are ones from Google or Facebook, and I can't find any option to add a photo for a contact.

I keep my contacts on the SIM, but when I copied one to the phone to see if that made a difference, it didn't, at least as far as I could tell.
Open the stock People app (i.e. navigate to your contact list) > select the contact > select Edit contact > select the camera icon in the top left corner. Your options are Gallery (find an image already on your phone) or Camera (take a picture of the contact). Hope it helps!