Sewing a Log Cabin block is fairly easy - just straight sewing. However, it is important to have an accurate 1/4" seam allowance. For my example, I'm using 2" strips and squares, but you can use whatever size you like. Traditionally, half of the strips are lighter and half are darker but I've seen gorgeous quilts made with all light tone-on-tone beiges/whites and ones made with only one color - like all your green scraps.
Here are the cutting directions for my example which makes a 10.5" finished block:
1 dark pink 2" square for the middle
1 white print 2" square
1 white print 2" x 3.5" rectangle
1 pink print 2" x 3.5" rectangle
1 pink print 2" x 5" rectangle
1 yellow print 2" x 5" rectangle
1 yellow print 2" x 6.5" rectangle
1 blue print 2" x 6.5" rectangle
1 blue print 2" x 8" rectangle
1 green print 2" x 8" rectangle
1 green print 2" x 9.5" rectangle
1 black print 2" x 9.5" rectangle
1 black print 2" x 11" rectangle
It is important to cut out the rectangles before sewing instead of just sewing a strip onto the center unit and then trimming off the extra. My mom made a log cabin quilt from a kit (this was before kits were even a thing!) and she decided to just sew the strips to the center unit and then trim it off. Well, we all know fabric can stretch a bit. Unfortunately, she would up not having enough of one of the fabrics to finish the last block - auugghh! We've probably all been there at some point. Good news - the company that sold her the kit had a comparable fabric that she used. Unless I look really hard, I can't tell where the odd fabric is!
First you sew the 2 squares together and press the seam allowance. For this block I recommend pressing the seam allowances away from the center of the block. It's also a good idea to check the size of the center unit after you press each seam.
Next you sew the 2" x 3.5" white print to the right side of the unit you made above.
Now you will sew the pink print 2" x 3.5" rectangle to the bottom of the unit you just made. You will continue sewing the rectangles to the center unit in a clockwise sequence until you've completed the block.