Remove the SATA cables before you attempt to remove the hard drive. Pull in the direction of the pink arrows.

You may need to lightly pry the hard drive out. The blue silicon was sort of sticky, and held it in.

Remove the light blue silicon "frame" from the HDD, and place it on the SSD. You'll probably have to try twice to get aligned with the right end going on the right end of the SSD.

You want to end up with your SSD attached with the SATA cables in a way that keeps the original fold in the ribbon the same way.