Paint one side and the edges of each trivet with white paint. Allow that to dry and apply a second coat if needed for complete coverage.
Working with one cork circle at a time, apply a medium (not thick) layer of Mod Podge over the top of the cork circle, making sure to get the edges.
Smooth the fabric over the Mod Podge, making sure to get all the way to the edges. If some comes through the fabric it's okay. Just wipe away any excess. Repeat with the remaining cork circles and let dry.
Apply Mod Podge to the top of the fabric. One coat is fine. let dry.
Cut around the edges of the circle with scissors, leaving about an inch or two of fabric all the way around. Then you're going to cut the excess fabric into tabs as you see in the photo, so that you can bend the fabric around the back to attach.
Apply Mod Podge to the edge of the back of the cork round and fold a tab over, smoothing down with the brush (and your finger if necessary).
Continue this step all the way around the cork circle, applying Mod Podge and attaching the tabs to the back. Repeat with all cork circles and let dry.
Glue down the wood using a strong, fast adhesive (i.e. super glue) where I planned to attach the strips. Allow the glue to dry. Attach your picture hanging strips to the wall and the wood pieces on the back of each memo board, following the directions on the package.