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A Grecian Square quilt block is a beautiful and intricate design that can add a touch of elegance to any quilt. Here are the steps to sew a Grecian Square quilt block:
Materials:
 Fabric in two contrasting colors (one light and one dark)
 Rotary cutter and mat
 Ruler
 Sewing machine and thread
 Iron and ironing board
Instructions:

Cut two squares of fabric in contrasting colors measuring 12 ½ inches each. These will form the base of your Grecian Square quilt block.

Place the squares right sides together and sew a ¼ inch seam allowance along all four edges.

Use your rotary cutter and ruler to cut the sewn squares into four smaller squares, each measuring 6 ½ inches. You should have eight squares in total (four in each color).

Take one square of each color and place them right sides together. Sew a ¼ inch seam along one side.

Open up the two squares and place the darker square face down on the ironing board. Press the seam allowance towards the darker fabric.

Take another square of the lighter color and place it right sides together with the darker square. Sew a ¼ inch seam along the opposite side of the darker square.

Open up the two squares and press the seam allowance towards the lighter fabric.

Repeat steps 47 with the remaining squares to create four halfsquare triangles in total (two in each color).

Arrange the four halfsquare triangles into a square, rotating each triangle so that the dark fabric forms a square in the center of the block. Sew the triangles together with a ¼ inch seam allowance.

Press the seams open or to one side, whichever you prefer.

Your Grecian Square quilt block is now complete!
Repeat these steps to create additional Grecian Square quilt blocks, and then arrange and sew them together to create a quilt top. Add batting and backing, quilt as desired, and bind the edges to finish your beautiful Grecian Square quilt!
This is a great technique for making half square triangles that eliminates the need to directly manipulate the stretchy bias of the triangle. It utilizes two easy to cut squares producing two half square triangles.
On the back of the lighter fabric, draw a pencil line, diagonally from corner to corner.
Stack a pair of light and dark squares, right sides together. Sew a 1/4 inch seam allowance on each side of the line.
You will end up with something like this.
Now cut along the diagonal line.
Press the seam together to set the seam. Then press towards the darkest fabric.
To trim the block to the exact size line up the diagonal 45°angle with the ruler on your seam.
And then carefully trim your block with a rotary cutter.
The secret to the nine patch is all about ironing seams so that they butt when they are joined.
Cut 5 A squares and 4 B squares in the required size.
Chain piecing, join a B square to only 3 of the A squares, right sides together, with a 1/4 inch seam allowance. No need to press just yet.
The result will be:
Next, take the remaining A and B squares and, chain piecing, join them to these units, right sides together, with a one 1/4 inch seam allowance:
Your result will be:
To make this faster you can cut strips.
Cut A and B strips for the appropriate width, and join them into A/B/A and B/A/B units. Note you will need twice the length of B/A/B strips, as there are two of these units. Once your strips are joined, right sides together, with a 1/4 inch seam allowance. Press every seam towards the dark fabric.
Cut across your prejoined strips to create the units needed for the nine patch:
You will achieve the same result as above, but this method is faster.
To make a standard 9 patch, the width of the unit cut from prejoined strips is the same as the width of the original strips.
Press all the seams to the dark fabric so that all the seems butt up.
Join the B/A/B units to your A/B/A units with butted seams, right sides together, with a 1/4 inch seam allowance.
The direction of the final, central seam is optional. But guided by the placement of the block in the larger scheme, and wherever possible, iron to facilitate budding the seam joints.
Wider Application:
Just as the 4 patch, you can apply this methodology to all kinds of 9 patch blocks. As long as the patch has an underlying 3x3 grid, no matter how many pieces, the basic principle applies. It is repeated over and over, each 9 patch laying adjacent to the next 9 patch. As long as you keep pressing seams in pairs of opposite directions, piecing will be smooth sailing.
Try these out. Each block has an underlying 3x3 grid, and can be pieaced as a 9 patch.
Sometimes it is not obvious which direction is the dark with complicated blocks like those above. Just remember the basic ironing plan is:
How to Resize Quilt Blocks: