I have always had luck with this recipe

1 cup light olive oil or safflower oil (I don't use canola it's inflamitory for me) and extra virgin olive oil is too strong of a flavor
1 egg yolk
1 Tbs water
1 Tbs fresh lemon juice
1/2 tsp salt
1/4-1/2 tsp mustard powder (this acts as an immulsifier so do not omit it)

Put all ingredients in a tall narrow container(oil,on top), let sit 15 minutes. With your immersion blender, start at the bottom and blend 5 to 10 seconds, as soon as an emulsion starts draw the blender slowly upwards to incorporate all ingredients. Total process takes about 30 seconds. Adjust lemon, salt and add tobasco if wanted. I have made this hundreds of times without failure.