How do I keep die cut leaves from looking flat on a wreath card?

Yes, the shading is basially ink sponged on the edges, and distress inks are perfect for it. I use one of those little foam blending tools or even a makeup sponge. Start with barely any ink, tap most of it off on scrap paper first, then work in circles from the outside edge inward using a light touch. Darker color right at the edge, fading toward the center. You can always add more but you can't take it off, so build up in thin layers. A darker shade of the same color family works best, like a rusty brown on the orange leaves or a deep red on the green ones. If it looks blotchy at first, keep circling and it'll smooth out.

For the edges lifting, the trick is a needle-tip bottle of liquid glue and one small dot right along the center spine, nothing more. I make around 60 fall cards every season for a local craft table and this is how I attach every single leaf. If a dot is showing through, your paper is just too thin, so layer two pieces of cardstock for the leaves and it disappears.

Also grab a bone folder and run it down each leaf before gluing, that curl is what sells the whole arrangement. And grab a fine brown pen to draw the veins on after sponging, takes ten seconds a leaf and suddenly they look real instead of punched out.

The other thing that instantly adds realism is veins, and you do not need anything fancy for them. I lay my leaf on a mouse pad and run an embossing stylus or even a dried-up ballpoint down the center spine, then a few short angled strokes off either side, and the paper actually creases into a gentle curve that catches the light. Follow each score line with a fine brown pen if you want the veins visible from a distance, since pencil-gray reads as dirt on autumn colors. Do the scoring before you ink the edges, by the way, otherwise the stylus drags the ink around and smudges it into the crease.

For the flat pile look, try curling the leaves a bit before you glue them down. I just run each one over the edge of my scissors blade like I'm curling ribbon, and it gives the paper a natural bend that catches light. Even a slight curve makes a huge difference once they're on the card. Also, don't glue them evenly spaced in that circle. Overlap them and cluster two or three togather in spots, let some hang off the edge of the circle a little. Real fallen leaves are messy, and the messy look is what makes it read as fall instead of a wreath.

Update: it actualy looks like a real wreath now. Ran each leaf over a scissor edge to give it a bend like one of you suggested, then used one small dot of glue along the spine so the edges lift without showing. Sponged a little rust ink on the tips too, barely any pressure. Sister's card is done and I'm making a second one for my mom.