After reading a lot about it and watching youtube explaining videos, I decided to finally answer this question. I hope I understood it right so that I can explain it right. It's a bit complicated so it's gonna take a while.
Cute Charm Glitch is a method for raising the chance of finding a shiny and it only works for Gen 4 games.
When you start a new game you are given an ID which is unique to you, but just in case you have the same ID and trainer name with another person, a Secret ID (SID), which you cannot see, is also given to you by the system, so that even if you trade Pokemon between each other the system will still tell the difference,
Every time you encounter a wild Pokemon, the system also randomly generates a Pokemon ID (PID or personal ID), which decides it's nature, gender and if it is going to be a shiny or not.
In gen 4 games if you have a certain combination of ID and SID and a Pokemon with cute charm ability in your party, your chances of encountering shinies is increased to 21.34%, which is what the cute charm glitch is.
Let's assume there are a total 100 PID combinations. What cute charm glitch does, is reduces the number of PID combinations you encounter to let's say 10, out of which 2 are combinations that give you shiny Pokemon. That makes your chance to encounter a shiny like 20%. That's how it works.
Now that you know how it works, you want to know how to find your SID, right? Right.
There are a few methods for calculating your SID and one of them is having a shiny Pokemon and putting his IV's in this program called RNG reporter. Link
There are also some action replay codes that can do the same thing without having a shiny. For more info just type in to google: How to find Secret ID.
Ok, so you have your ID and SID. How do you know if the cute charm glitch is going to work?
There is this tool called the CCCalc that is going to tell you that. Link
Just type in your ID and SID and it will tell you if cute charm glitch is going to work for you.
It will probably tell you that it is not. There's only 0.01% of chance that you get a matching ID and SID for the cute charm glitch to work. YES 0.01%
So how do you get a combination of ID and SID for the glitch to work?
That is done by a method called RNG Manipulation (Random Number Generation). And that's what the RNG Reporter program is really for.
Now you might think that when you start a new game, the system randomly gives you a trainer ID, which is impossible to predict since it's random. That is not the case here. Your trainer ID is calculated through an algorithm which is different for each gen. In gen 4 however the ID you receive depends on the time on your DS and the delay time, which is the time you take to go through the intro part in which the Pokemon professor tells you about the world of Pokemon.
From here on I cannot help you anymore. You need to completely read the guide in smogon