(Update 1/9/2018: Interested in more about this ritual? Check out my more polished, fleshed-out writeup over on this page!)
Well, if it weren’t for the fact that it’s entirely overcast, I’d be outside right now under the light of the full moon doing a short and simple ritual. Tonight’d be a fantastic night for it, too, since the Moon is at its perigee, its closest point to the Earth, so it’s also huge. Fie on the weather! The only cop-out (cop-in?) I’d be able to get is if it started raining; the angel of the Moon once suggested that if I can’t get moonlight, moonrain is just as helpful, since the moonlight comes in contact with the clouds and the clouds transfer that light to Earth in a more material way. Next month might be better, since the full moon will occur on a Monday, so I can get it to its own day and time, assuming that the weather will allow for it.
Anyway, the ritual I use for full moons is short and simple, taken from the Greek Magical Papyri (VII.317). On the night of a full moon, go out to a dark place outside where you can see the Moon. Purify oneself in the moonlight however one sees fit, then say the following:
ΑΧΘΙΩΦΙΦ ΕΡΕΣΧΙΓΑΛ ΝΕΒΟΥΤΟΣΟΥΑΛΗΘ ΣΑΘΩΘ ΣΑΒΑΩΘ ΣΑΒΡΩΘ
AKHTHIŌPHIPH ERESKHIGAL NEBŪTOSŪALĒTH SATHŌTH SABAŌTH SABRŌTH
State your request and intent to the Moon aloud, whether something general such as for protection or for something specific for a particular working. Make an offering to the Moon, then close the rite as you see fit.
The names are related to very dark, chthonic, or nighttime-related spirits, as can be seen by the name of Ereshkigal (in a Greek form) in the words. Jason Miller uses a variant of the first three words in his spirit trap design, too, and this working is under a heading in the PGM specifically for protection. However, I use this as a general working, with protection as it main focus.