After measuring out where we wanted the entire piece to be, I taped the portion where I wanted the chalkboard to be and painted it with chalkboard paint.
Once dry, I worked on the corkboard. I purchased cork squares from the dollar store and, after a few experiments with different glues, I used caulking to adhere it to the wall.
To keep the pieces in place while they dried, I only tacked on a few at a time. Then used painters tape to prevent them from falling off the wall.
Once I had on the pieces, my husband added some trim to match what we had in the room. And also a notched trim which he attached with L-brackets to the bottom for holding chalk.
I love it! And, obviously, my kids do too.