How to Chain and Web Piece for Matched Seams!
The Cleo pattern takes advantage of web piecing, which is like chain piecing's cool older sister. To chain piece, you simply piece without cutting the thread between seams. Usually it's done by sewing all the same part of a block together in every block of that type, whether in the whole quilt or a specific section like a row, or it could also refer to sewing things together into rows. Web piecing is a more advanced version. It's great because it's faster than doing every seam individually, it saves thread because you have shorter, if any, tails, and it can help you stay organized! No more upside down sections in that one block you missed.
Web piecing works best when you have units of the same size to sew together, like in a nine patch. That's the example I'll demonstrate with. I'll use 9 different colors for each block so you can tell what's what. Start by laying your pieces out. It's easier for me to do this as a visual person, but if you don't need to you can keep your pieces in piles or whatever method works for you.
1 2 3
1. Start by sewing each square in column 3 to its corresponding block in column 2. If you usually end with your needle down, you'll want to have it end up for web piecing.
Place the light blue fabric right sides together with the light pink fabric, blue on top. Sew the light blue to the light pink square. Do not cut your thread. Lift your presser foot and pull the finished piece out so there's around 3/4" of thread behind the needle. Place the medium blue square right sides together with the medium pink fabric, blue on top. Pop it under your presser foot and sew that seam. Repeat for the dark blue and dark pink fabrics, 3/4" of thread between. Cut the thread. (This is chain piecing!)
2. Press your squares open - do not cut the thread, and alternate pressing to each side. In the image below, rows 1 and 3 are pressed to the blue and row 2 is pressed to the pink. They are still connected by thread.
3. Repeat step one, this time sewing column 1 onto the column 2/3 units, keeping the greens on top. The nine-patch unit will look like this, with the three rows sewn together and each attached by the seams.
5. Press the same way as in step two. Do not cut any threads yet, and press each row in the same direction as you did in the previous step, alternating between the rows, like so. It's now a web instead of a chain! 
6. Now for the fun part - we're going to sew the rows together by nesting our seams. Match row 1 unit to row 2 unit right sides together. Butt the seams up against each other so they lie flat. Pin at each seam to keep them in place. Note, your units should be the same size; I've made the top one smaller for the sake of clarity in the illustration.
Once sewn, you may press the seam whichever way you'd like although I recommend pressing open if possible. Consider what units that seam will connect to if you'd like to continue nesting (or even chain or web piecing with larger units). You will likely need to clip the threads connecting rows 1 and 2 in order to press properly. Leave the unit attached to row 3. 
7. Match row 3 unit to rows 1/2 unit right sides together, with the row 3 unit on top. Butt the seams up against each other so they lie flat. Pin at each seam to keep them in place. 
Once sewn, you may press the seam whichever way you'd like although I recommend pressing open if possible. Consider what units that seam will connect to if you'd like to continue nesting (or even chain or web piecing with larger units). You will likely need to clip the threads connecting rows 2 and 3 in order to press properly.
The finished unit should match seams quite well if you were careful nesting, and short thread tails so you don't have to worry about trimming them later!