The Nine-Patch quilt block is probably the most used block in the quilting world. It is very easy to sew and sooooo many blocks use the nine-patch layout in construction.
The most basic way to sew the block is to arrange 5 medium/dark squares and 4 light squares as shown. (Or arrange 5 light squares and 4 medium/dark squares for a different look.)
Sew the squares into 3 rows (or columns as shown here). Press the seam allowances toward the medium/dark squares. Usually seam allowances are pressed toward the darker fabric to prevent show through on the quilt top. Also, pressing the seam allowances in opposite directions means that when you sew the rows/columns together, the seams will nest together nicely and makes for nice intersections that lay flat.
Sew the rows together. Press seam allowances toward the inside of the block. Trim/square up the block if necessary.
Here's a picture of the back of the block that shows the pressing directions. As you can see, the seam allowances on the left and right sides are pressed toward the outside of the block and the top and bottom seam allowances are pressed toward the inside of the block. This also helps when sewing the block into the quilt because you can rotate the block so that seams will nest with adjacent blocks. I hope that makes sense to you - it's a bit hard to explain.
You can also sew a Nine-Patch block using the strip piecing method. Sew two strip sets the same way as for the Roman Stripe block. You will need a dark/light/dark strip set that is twice as long as a light/dark/light strip set. Press seam allowances toward the dark fabric.
Cut two units from the dark/light/dark strip set and 1 unit from the light/dark/light for every Nine-Patch block you are making. These units will become the rows of the block. Cut these rows to the same width as the strips used to make the strip sets. For example, if you used 2.5" strips to make your strips sets, cut these rows at 2.5" wide as well.
Lay out two dark/light/dark rows and one light/dark/light row as shown. At this point, it the same as the first example shown above.
Sew the three rows together to make the Nine-Patch block. Press the seam allowances toward the center of the block. Trim/square up the block if necessary.