First put soy milk and oil together in a container, then puree briefly (5 - 10 seconds) with the hand blender until a cream of the desired firmness is obtained. It probably works better when the oil and soy milk are at the same temperature, and lemon juice should also be helpful if the oil does not bind properly - but I mostly ignore both and have not had any problems so far.
Then season the whole thing with salt (about half a teaspoon, I always do it by feeling) and pepper. If you want, you can also add vinegar, mustard, maple syrup or the like.
For aioli, chop 1 clove of garlic (or two) and mix in.