This is how I make it in our Thermomix:
Blend together on high until the almonds have disintegrated. You will still see some chunks of dates at the bottom though. I usually heat mine while I blend in the Thermomix so the dates go soft and make the milk sweet. You could always use hot water for this instead.
Lay a piece of muslin cloth over a strainer which is resting over a large bowl. Pour the mixture on the cloth and let it strain. Squeeze out the excess.
You will have lovely, creamy almond milk in the bowl and almond pulp in the cloth. With the pulp you can google how to dry it out in the oven or dehydrator to make almond flour, or you can use as is in cracker/cake/muffin recipes (also google!).
I store our almond milk in a glass jar with a lid in the fridge for about 5 days.