The full moon this weekend (the full moon was actually last night) will be the biggest in about 20 years, but if you try photographing it with anything shorter than a 300mm lens it is still going to look small. The technique of photographing the moon is pretty simple. For exposure use the sunny F/16 rule, since the moon is being lit by direct sunlight, it doesn’t matter that you are in total dark of the night – the moon isn’t. So if your ISO is set to 200, the exposure should be 1/200s and f/16, set your camera to manual exposure for this. I would suggest bracketing the exposure a stop/shutter speed.
Use a tripod and cable release in order to get the sharpest possible picture. You will probably find that you will have to continually reposition your camera/tripod as the moon “races” across the sky. Depending on your camera make/model you may have to switch off the autofocus and manually focus the lens, if it is having trouble focusing as it searches back and forth for something to lock the focus on.
Good luck and hopefully you will have clear skies!