The trick with sewing quilt blocks is to find the short cuts that speed up the process. The Shoofly beginner quilt is made from only 25 blocks but even that can take quite some time.
First of all lay out all the quilt block pieces as they will appear in the finished quilt block. I usually make piles of about half a dozen of each piece to work from.
Quilt blocks are usually sewn from top left across the top row. Then each row is sewn together and finally the rows are sewn to each other. However in this quilt block there are 4 squares made by combining a white and blue triangle and it makes sense to sew these squares first.
With right sides together and using a 1/4" seam, sew a blue triangle and white triangle together along the long edge. Chain sewing quite a few of them saves time. Click on chain sewing for more information.
Now take a blue square and sew it to one of the triangle squares, again with right sides together and using a 1/4" seam.
The 1/4" seam is important because if your seam width varies then your blocks will not fit together neatly.
Add another triangle square to the other side of the blue square and your first row of the quilt block is complete.
The middle row is straightforward enough: a blue square either side of a white square.
The 3rd row of the quilt block is the same as the 1st row, but just positioned upside down compared with the 1st row.
In order to sew the top row to the middle row, flip the top row down over the middle row, right sides together. Pin at each seam so that you know that the seams from each row match each other and that the seam allowances on each row go in different directions from each other to reduce bulk.
Now sew the 3rd row to the top 2 in the same way.
I was going to sew all the quilt blocks the same, but I swapped the colours on one block to add a little interest. This will be the centre block.