Cut the rind off the watermelon and then cut it into bite size chunks.  Place watermelon into a blender and blend for about 1 minutes, until it’s completely liquid.  You may need to help it get started at first but eventually it will all blend.
Place a mesh strainer over a large bowl and pour watermelon juice in the strainer.  Let juice drain out.  You can pick up the strainer and rock it from side to side to encourage more juice to come out

But you don’t want to use a spoon to press down everything in the strainer.  If you do that it will allow some of the pulp to get through and you don’t want that.  Once it’s just pulp left in the strainer you can dump that out and strain the rest of the juice.
If there’s lots of bubbles on top of the watermelon juice, or if some of the pulp got though, use a spoon to scoop it off the top.  You may want to let it sit for a few minutes to let things settle down before doing this.