Here are the questions you should ask yourself at this stage:
Do I have a solid grasp of the basic science underlying my idea?
Everything in science rests on the fundamental fields of physics, chemistry, and biology. If your exposure to one or more of these fields is limited to high school introductory courses, online reading and pop-science books, it would be an excellent idea to take a full year-long for-majors sequence of introductory courses in that science from a regionally-accredited college or university. It is best to make sure the physics course is calculus based; it is critical to do so if you will be working with physical science ideas. If you can identify the specific fundamental science with which you will primarily be working, it would not be a bad idea to take two different versions of the course, separated in space or time, so that you can be introduced to different viewpoints and ways of understanding the concepts. Most future scientists take an advanced course in their science in high school and then go on to take the introductory sequence at university.
To those who may feel a certain lack of trust in the scientific establishment: Please allow me to assure you that you can trust the content of these introductory courses. The science introduced here is truly fundamental, time-tested and solid. You will work in labs performing experiments to help demonstrate to yourself the validity of the theories presented. However, the entirety of human civilization is effectively a laboratory for these basic theories; these are the aspects of science to which we entrust our lives, our finances, and our precious memories on a daily basis. These are the theories on which airplanes, bridges, heart transplants, compact discs, electrical power systems, blood transfusions, antibiotics, computers, and food crops are built.
To young people and those without access to college courses: You can, of course, do some science without any formal education whatsoever. There are still a few unresolved questions of the sort that can be understood and worked with by high school students and interested laypersons, and there are any number of existing theories that could use some more experimental validation. And a great deal of the science involved in many interdisciplinary fields can be understood fairly well through dedicated self-study, provided that you have the capacity to read and understand introductory-level science textbooks. However, popular science books and the Internet will not provide an adequate background; you will need to seek out and work through books intended for students in the field.
Do I have a solid grasp of the basic mathematics used in science?
There are three basic types of mathematics used in science: algebra, calculus and statistics. The extent to which each of these is used, and the extent to which other types of math may be involved, depends on the specific variety of science. However, you will not be able to escape the need for math entirely. The math required for your introductory science courses or that which you find yourself needing to learn for your self-study program should be largely sufficient, with one exception: you will need to know some statistics to work with experimental data (yours or anyone else's).
Does my idea still fit with what I know about the world?
Now that you know some basic science and math, come back to your original idea. Is it still consistent with what you know about observed reality? If not, you may want to go back to the beginning and build a new conjecture, or you may want to refine your existing one so that it is consistent and possible. This is a personal decision that depends on the type of idea you're working with and how you feel about it.
Would I be satisfied if it turned out I were wrong?
This is a critically important question. Science does not prove positives; the best you can hope for is to gather a mountain of evidence to prop up your idea. It does, however, prove a whole lot of negatives. If you decide to enter your conjecture into the marketplace of scientific ideas, the odds are excellent that it will be partially or wholly disproven, modified, discarded, and/or replaced. At the rate that science has been moving in the last century, the odds are fairly good that this will happen within your lifetime. You should only consider treating your conjecture scientifically if you not only accept but look forward to this eventuality; in science, being "usefully wrong" is an accomplishment that helps humanity move forward in its journey toward understanding the universe more completely.
Can I formulate my conjecture in such a way that it makes measurable predictions?
It's okay to get stuck here for a while. What you're looking for is a formulation along the lines of:
"Under conditions (X, Y, Z...) outcome Q will be detected (more/less) often than would be predicted by (chance/existing theory)."The "more/less often" part here is important. Your prediction doesn't have to be accurate every single time; it just has to beat the accuracy rate of either pure chance (if there's not currently a theory addressing the situation at hand) or the existing theory.
The observation that helium balloons and hot air rise in the Earth's gravitational field does not invalidate the theory that masses are attracted to other masses; it just means I've failed to identify a confounding variable (the Earth's atmosphere).
The observation that individuals with clearly maladaptive traits occasionally reproduce does not invalidate the theory of evolution by natural selection.
The observation that some years are cooler than previous years, or that some specific regions show a cooling trend, does not invalidate the theory that increased carbon dioxide in the atmosphere leads to increased average global surface temperatures.
If you've conjectured that some people are capable of telepathy, the fact that your telepath occasionally fails to accurately identify what another subject is thinking doesn't necessarily invalidate the whole idea (but you'll have to beat the accuracy rates predicted by both chance and current psychological theories of face/tone of voice reading, possibly by eliminating confounding variables by placing your subjects in different rooms).
As I said, it's fine to get stuck here. It will take some time to figure out what exactly it is that your conjecture might predict, what the current theories in the field are, what they predict, and how your predictions are different. Do be aware that it's perfectly fine (and usually desirable) for your conjecture to predict most or even all of the same things that current theories do, but it does have to set itself apart in some way. If it makes all the same predictions as the existing theory and no new ones, the only ways it can set itself apart are:
- by uniting and reconciling two conflicting theories (like the Standard Model of particle physics and general relativity). In this case, the theory would in fact make some predictions that differ from those made by each of the existing theories, although it's possible that it would make no new, unique predictions. This is what string theory is trying to do. However, it's struggling to gain acceptance, specifically because it's nearly impossible to validate it as the correct unification because it makes no new, unique predictions. (I'm oversimplifying, but that's the general gist of the problem)
- by being simpler and more elegant than the existing theory, while encompassing all of its predictions. This is, in theory, a nice sort of thing to develop. However, it turns out that when we make theories simpler and more elegant, they often do end up predicting more, because they're more generalized. Newton's laws of motion and universal gravitation were not only simpler, more elegant formulations of Kepler's laws of planetary motion, but also served to predict the motion of objects on Earth. So if you have a conjecture that's simpler and more elegant than the commonly-accepted theory, take a step back from it and look at things it might apply to outside of the realm of the current theory; odds are you'll find it's more general and does in fact make some new predictions.
This one can be tough too. The real world puts limits on what we can currently test. If the difficulty in testing your conjecture is purely technological - if you can imagine a way to test it if we had infinite energy, better telescopes, better microscopes, better brain imaging, better dating techniques, or fully-equipped zero-g labs - then you've probably got a testable hypothesis, and you should talk to other scientists about how you might be able to test it indirectly. If the difficulty is definitional - if it's built into the definition of your conjecture - then you may have a problem. Specifically, if you're postulating extra dimensions that can't be detected, beings that exist outside the observable universe, extrasensory perception that only works when the subject isn't being observed by scientists, or miracles that happened at some time in the past and left no physical evidence, you're probably dealing with a subject that science isn't equipped to handle.
Now, there are some cases where the difficulty in testing appears to be definitional but is actually technological. If you're predicting the existence of an invisible pink unicorn, it would seem that you'd have a definitional problem - but if your IPU has mass and leaves footprints, or if it's tangible, or if things slow down when they pass through it, and if you have a general idea of where to look for it, then it doesn't matter terribly much that it's invisible except when you're trying to demonstrate that it's pink. This is the case with physicists' search for dark matter, a subject about which we appear to maybe possibly be getting some direct evidence in recent months.
Congratulations! You've got a testable hypothesis!
If you've made it past all those hurdles, your conjecture is now a testable hypothesis. You know the background science, you know what your idea predicts, you know how to test your predictions, and you're ready to go check them against reality! On to Part 3: The Infinite Degrees of Wrong.