I would like to know about the diffrence between a real emrald stone or a fake emrald stone.

Here's some general information about real emeralds: Emerald

Unfortunately, the market is littered with emerald fakes or doublets (stones that look similar to emeralds). Also, it is difficult to find an emerald without flaws (or a completely clear emerald), so be sure to not dismiss some stones just because there's a flaw. Some jewelers, however, cover some heavily-flawed emeralds with oil, which masks most of the flaws. Be careful of this

Then also, there are synthetic emeralds, which are technically real, but were manufactured in a lab. Here is a blurb about those types: Emerald - Wikipedia, the free encyclopedia

Essentially, I was unable to find any specific things to look for when verifying an emerald. But be sure to always buy from a reputable jeweler/dealer and if you already have a piece, have it appraised by a local jeweler. They are excellent at spotting fakes and doublets.

Good luck!