Making almond milk is actually an incredibly old process. We learned about it in culinary school as part of our training in Classic French cuisine, but it was made and used long before the French transformed it into delicate blancmanges.
The process essentially involves soaking almonds in water over night or for up to two days — the longer you soak the almonds, the creamier the milk will be. Drain and rinse the beans from their soaking water and grind them with fresh water. The resulting liquid, drained from the almond meal, is almond milk.
Real, fresh, very tasty almond milk. It's a world-changing thing.
Homemade almond milk only lasts a few days in the fridge, so make just what you think you will drink in this time period. You could heat your almond milk on the stove to pasteurize it and extend the shelf-life, but this somewhat defeats the purpose of making it yourself. The process of grinding and straining the milk only takes a few minutes, so making smaller, more frequent batches doesn't feel too labor intensive to me.
Start with a ratio of 1 cup almonds to 2 cups water when making almond milk. This makes a milk that is roughly the consistency of 2% milk. If you'd like a thinner milk, use more water next time; thicker, use less.
I have made almond milk in both a blender and the food processor, and I've had good results with both. Overall, I like the milk made in the blender every so slightly better: it has a silky texture and a subtly sweet flavor. Milk made in the food processor is a bit thicker and occasionally has some grit, and it has a more pronounced nutty flavor. Visually, you can't tell the difference at all! If you have both a blender and a food processor, try making almond milk in both to see which one you prefer.