The full moon is a time when major workings should be performed. This is the climax of the moon's power, so you should take advantage of it as it can make your spells even more powerful. The full moon also relates to fertility, one interpretation of this can be seen by growing plants as the moonlight pierces the ground. If your like most witches and can't do a full on ritual with candles and what not, you can meditate to any of the mother goddesses, such as the Egyptian goddess Isis, or Demter the goddess who brings us the four seasons. I know technically it's her lack of doing her job which brings us winter but I still could that as her giving us winter. These are only two of many mother goddesses you can meditate to if you want to do something for the full moon.
Other information about the full moon: the full moon occurs when the moon reaches its zenith, this makes the moon appear like a silver circle in the sky. Spells that should be casted during the full moon are spells for transformation, increasing psychic abilities and fertility (as previously mentioned) just to name a few.
Note: spells are still just as powerful even without the aid of the full moon, the full moon just increases the power of your spell, so know that you don't need the full moon for your spell to work.
There are many more things that can be done during a full moon besides spells. The moon has a massive amount of symbology varied throughout many cultures and there is no dispute that it effects everyone. It is a wonderful time to recharge yourself, crystals, candles, and so on.
You don't have to meditate on any deity at all unless you'd like to. It's the full moon so meditate on the full moon. Think of how big and encompassing it is. Think of the way it fills you and charges you making you feel spry and young.
Oh yes of course. You don't have to cast spells during the full moon, I was just trying to have "what you can do in relation to spells during the full moon" be the main point of my post. Thank you for including your input!
P.S I know is reply is "late" it's just that life had me busy.