It would depend on the size of the headpiece it may attach too.
I have made button hole stitch loops on the edge of satin ribbon that I bound the veil into, that you then loop onto a headband and sit under the piece, or grip into the hair under the piece.
Others I have seen use small pieces of (velco) touch and close in places to hold it in place and remove later.
Others may have better ideas than mine.
I have done this before for a friend...she wanted to detach the birdcage veil after the ceremony, so under the base I used sticky velcro dots & the veil was attached to each side using the velcro & attached to the base. My friend said her bridesmaids easily removed the veil for her. May not have looked terribly neat underneath but it worked a treat. I hope tgat makes sense?
I generaly make 2 different accessories:
- one the brooch with a comb or any other attaching system
- the veil, with another comb, that I embelish a little bit, a delicate touch
And like that they can wear them together, just the veil or just the brooch
I usually make them completely separate.
It's worth chatting to hair stylists about how they attach pieces for brides, because I was using metal combs & my cousin had her hair done at home, & the stylist started complaining about the type of comb, not realising I had made the veil & headpiece.
Anyhoo. With a birdcage I make little cotton loops to pin on with an everyday bobby pin or kirby pin(UK). That way it's super easy to remove & usually easy to hide.
The headpiece with have a comb or alligator clip depending on the style or size.
With veils, I sew them onto the the elastic loop trim that seamstresses use for buttoning up the back of the dress. They it can just be slipped onto the decorated comb & then taken off just as easily after the ceremony/photos.