What are the effects of me not eating (fasting) every so often for maybe a day at a time?

Decrease: Your metabolism decreases when you occasionally fast as your body thinks it needs to retain resources rather than use them.

Minimal: A number of people as a behavioral modification or attempt at self discipline will fast one day per week. This will cause no harm. You should be mindful of proper hydration so water intake probably should not be a part of this but ingestion of nothing solid certainly will not hurt you.