Place the egg yolks, mustard, vinegar, salt and pepper into a medium-sized bowl.
Place the bowl on top of a damp cloth (to prevent the bowl from moving when you are whisking later).
Mix the ingredients together with a whisk or a wooden spoon (I recommend using a whisk).
Very slowly whisk in the oil, drop by drop, and keep whisking until the mixture starts to thicken and emulsify. You may need to alternate between adding the oil and whisking vigorously to make sure that the mixture stays emulsified.
Once all of the oil has been added, taste for seasoning. I often like to add some fresh lemon juice to taste, but you could also add a touch more vinegar if you need to.