I have been trying to find Emeralds underground. I could not find a village nearby, and I really want to get Emeralds. How rare are they? And is it possible to not get them one by one?
According to the wiki entry on emeralds, they are indeed quite rare.
First of all, they only ever generate in Extreme Hills biomes, so make sure you are actually in one (You can check the biome you are in easily by pressing F3, it's displayed on the left).
The game attempts to spawn 3-8 single pieces of emerald ore per chunk (16x16 area), between y-levels 4 and 32 (like gold), but those attempts are not necessarily successful, so there might be less.
The only way to obtain more than one emerald at a time without villager trading is to use Fortune-enchanted picks. When using a Fortune III pick, you can get up to 4 emeralds from a single ore block.
I personally do not have a good version but I do have a lot of knowledge on the topic. I have watched many people playing by video and understand that emeralds usually spawn with a chance of 1-3 in one area. I also know emeralds only spawn in the Extreme Hills Biome only (other than any variation of Extreme Hills)! We do not have a good chance of emeralds!