Every full moon is worth marking, but two specific variations get treated as bigger occasions, and both have a real astronomical basis underneath the folklore layered on top.
Blue moons
Most commonly, a blue moon is the second full moon to fall within a single calendar month, which happens roughly every two to three years: the actual origin of "once in a blue moon" as a phrase for something rare. A less common definition, used by some almanacs, calls the third full moon in a season with four (instead of the usual three) a blue moon instead. Either way, the moon isn't actually blue; the name is about rarity, not colour.
Because a blue moon is essentially a bonus full moon, it's often treated as a good night for ambitious or overdue workings: the goal you've been putting off, the wish that felt too big for a regular month. There's no special technique required, just an awareness that you're getting an extra full-moon night that month.
Supermoons
A supermoon is a full moon that coincides with the moon's closest approach to Earth in its orbit (perigee), making it appear up to about 14% larger and 30% brighter than an average full moon. Several happen most years, usually clustered together.
Folk practice treats a supermoon as an amplified full moon: stronger for charging tools and crystals, stronger for big manifestation work. Worth knowing: some people also report feeling more emotionally intense or overwhelmed around a supermoon, whether from the extra brightness disrupting sleep or simply expecting a bigger effect. Pace yourself the same as you would with any unusually charged night, and don't feel obligated to do more ritual than usual just because it's a supermoon.
How to know when one's happening
Neither of these is obvious just by looking up, the way an eclipse or an ordinary full moon is: a moon phase calendar or almanac app is the easiest way to know a blue moon or supermoon is coming before it arrives.
