Begin by making a careful choice of your container, which could be the same for all the different signs and phases of the moon, or which could vary as the moon does - sometimes large and sometimes small, sometimes bright and sometimes dark. You might even have twelve different ones corresponding to the astrological signs.
Your container needs to be able to hold as much water as you would use up in a month, drinking one sip a day. And, you need to be able to close it tightly, so your moonwater won't evaporate.
On the eve of the full moon, fill the container with fresh water. If you like, add a piece of jewelry or a stone that corresponds to the moon's sign. (I don't have any rules for this, but freely associate what the different signs symbolize.) During the full moon, the moon's sign is opposite the Sun's sign.
Expose your filled container to the full moon for the entire night. Place it outside and in the open where the full moon can shine into it for as many hours as possible. Next morning, take your first sip of moon water. This water that has gathered the moon's energy will be the first thing we consume every day from now until the next full moon. Each morning, on an empty stomach, one more sip is consumed, and we strengthen ourselves with the properties of full moon: creativity, abandon, imagination, wildness, strength, brightness.
I wish you much joy with the water of the moon!