If you are interested in accurate models of reality, there is only one method you should be using: the scientific method. Like atheism, this is much simpler than most people seem to think, and is not some government conspiracy consisting of men in white coats in secret labs. Everyone uses the scientific method almost constantly, but they may not be aware they are doing so.
The scientific method uses reason and evidence to gather information, and uses that information to make informed, sensible decisions. We remain sceptical (doubting) of any proposition until it has been demonstrated to be true beyond reasonable doubt, repeatedly and independently. This means anyone should be able to reproduce the results. This is the most formal version of the method at its most sophisticated.
You don't have to be doing any sort of advanced science to be using at least an approximation of the scientific method (what I would call science-esque). Of course, when you're doing detailed research you're going to be exact about everything; but in everyday life, we use a version of the scientific method all the time. Every time you set your alarm clock, every time you do some cooking, every time you walk through a doorway rather than into the wall, you are using the scientific method. To approach these tasks in any other way would be insane. Would you randomly pick a time for your alarm clock, ignoring what you know about how time works? Would you put twice as much of an ingredient into your cake just in case half of it disappears? Do you walk towards the wall, having faith that you'll be able to pass through it instead of using your reason and evidence to use the doorway? Even something as simple as a child screaming to get attention is an application of the scientific method at its most basic. The child has noticed a trend in the past where screaming gets the result it wants, so it repeats the behaviour to get the same result.
You use this method all the time, if you didn't you wouldn't be able to function. It is the only known method for obtaining consistent, reliable results. Either you are using a method with some sort of consistency and reliability, or you are not. And if you are not, then you cannot possibly know what to make of any "results" you think you are getting. Even people highly skilled in the use of this method abandon it altogether when it comes to their religion, superstition or "spiritual" matters.
On the subject of religion and the supernatural, I often hear people talking about "other ways of knowing things". There are clear problems with these "other ways". Firstly, they seem to rely entirely on personal experience which cannot in any way be reproduced by others for verification. Secondly, the results vary wildly from person to person. Both of these problems indicate that the person is not thinking clearly, and is using a mixture of poor logic and innate bias to come to conclusions they already want to be true. There has never been a clear process put forward for this that makes any sense.
People sometimes try and say that this method "doesn't work on everything". Common examples are emotions. How can I tell if someone loves me? Can I measure it scientifically? Even though this is not as simple as just getting a ruler out, you can indeed still use scientific methods. At a physical level, brains can be scanned to examine configurations which can point to certain emotional states. On a day to day level, you gather evidence from the way a person acts. If they take care of you, are nice to you, seem sincere when they express their love and don't do anything harmful, it would be a fair assessment that they do indeed love you. If you then find them stealing your posessions or cheating on you, this is clear evidence to the contrary. So although you aren't dealing with simple numbers, you are following a logical method based on weighing up evidence. What you are not doing is just coming to random conclusions based on nothing, as people seem to be suggesting when conflating emotions with religion. If religion/spirituality did demonstrate anything about reality in a reliable way, then it would be a science.
An important thing to note about the scientific method is that it doesn't deal with absolute certainty. Science builds the best models available, and comes to tentative conclusions about reality based on probabilities. However much information you have collected, there is always the chance that there is some underlying problem you have missed. If such a problem becomes apparent at a later date, then the models are reconsidered, and new ones are put forward. Science adapts to the best available evidence.
Science deals with the material world, leaving the abstract to philosophy.