Beginning with the basque, I neatened the seam edge: First fold 5 mm over, press with an iron and machine stitch, then placed the two neatened edges right sides together and run a seam half way. At the waist edge fold 5 mm over, press it then fold 10 mm over again, press it then machine stitch it to form a casing for the elastic.
Then I added the lace to the bottom frill, seamed the back as I did for the basque, but all the way from the bottom to top. To gather, run two rows of stitching (set on longest stitch and securing at the beginning of each row but leaving the end threads) about 5 mm apart. Pull the underside threads up until the gathered edge matches the basque.
Pin the two right sides together, easing the gather to fit the basque evenly, then run two rows of stitching around before neatening the raw edge with a small zig-zag stitch.
Turn your garment the right side out and it should look like this.
I added a further row of lace just above the seam between the basque and frill, over lapping the end and turning the edge under so no raw edges showed.
The final touch is to thread elastic through the waist casing, stitching the ends of the elastic securely so it doesn't pull through, then stitch a press stud (snap) on to close it at the back.
You may also find this a useful tutorial to make a tiered skirt.