The first step to understanding the agile methodology is to understand that there is no such thing as the agile methodology. If being agile were as simple as following a new methodology or process, you'd probably be doing it already.
Being agile is much more about changing your mindset, about seeing the world differently and applying different thinking to the problems that you encounter. The best way the mindset has been summed up is in the agile manifesto, but the important thing to remember is that agile is about responding to change, constantly looking at what is happening around you and using that information to decide what to do next. This is something agile people often call 'inspecting and adapting'.
This approach applies both to the work that you do, and how you do that work. So as a result, how you do your work should be constantly changing based on what you learn from the work you've just done. This means there can never be an agile methodology, as everyone's application of agile should be unique to their specific context, based on what they learn about it.
That said, there are many agile frameworks that give you tools and techniques to use which help bring the agile mindset to life, and for many people they're a good place to start. However, a framework is not a methodology. A methodology tells you what to do. A framework gives you principles and practices you can use as a appropriate in your own context.
That's the true challenge of becoming agile. Finding out which principles and practices help you constantly inspect, adapt and respond to change in your own specific context.