I've found the good old food processor to be the easiest method to get the consistency you want.
Put your soap in the processor first and grind till a pretty fine powder (this may take a few minutes, patience). Then add in your Borax and Washing Soda, pulse till well mixed, pour into a storage container and wahla! Laundry detergent. For powder, as per usual, you start the water on your machine, add in approx 2-3 tablespoons of powder, then the clothes. A little goes a long way. I've never tested this in an HE front loader, so check your warranty information, but for the standard top loading washer, works like a dream.
I often add about a cup of baking soda to this mixture because I have a toddler boy and smelly dogs, and this provides extra deodorizing power, though the original recipe works fine for most stuff.
The soap you use is up to you. Traditionally something like Fels-Naptha or Ivory is used. I prefer an organic low ingredient brand like Kiss My Face, or other natural brands. The one in this picture is a dead sea soap, and has a beautiful vanilla almond scent.
Happy Cleaning Y'all!