Rinse almonds well in a strainer (as you would rice), then pour into a bowl, cover with water, and soak overnight (this makes the resulting milk more digestible).
Drain almonds, rinse again, and put in a blender with 3 cups water. Add the dates, vanilla, and salt. Blend on high speed until very well blended, about 3 minutes. Strain almond milk through a nut milk bag or large, doubled piece of damp cheesecloth set over a bowl and carefully squeeze to get all the liquid out. Discard pulp.