You need a very strong, powerful blender.
ingredients for 400 ml
125 ml soy milk
250 ml oil (neutral flavor, such as canola oil)
2 tsp lemon juice
1 tsp mustard
1 tbsp vinegar
1 tsp sugar
Pour the soy milk into a tall container (blender-appropriate), fill the oil into a jug from which it can be easily poured.
Now mix the lemon juice with the milk. Blend at highest level pouring in the oil very slowly. It takes a while, but ensures that you get a good emulsion of soymilk and oil.
If all the oil is poured in, add the remaining ingredients and mix again.