Everyone can do science. Most people, especially younger children, do so on a routine basis. Science is just finding out more about the universe around you. Infants playing peekaboo are conducting a profound experiment. They cover their eyes and everything vanishes. When they uncover their eyes, everything is back. Wow! Things have persistent existence! Even if you can't see them, they're still there. Then you cover your eyes, and the child can still see you. Existence continues. Whoa. Elaborate the game. One of you hides behind something. Then pops out. Whee! Things continue to exist even with your eyes open, even if they pass from view. No wonder children giggle at the game. This is a profound discovery about the nature of the universe.
In similar vein, we can all speak prose in our native languages, or run. The thing which becomes a question later along is whether you are doing it at professional level. I run, for instance. Most of us can. And, with appropriate training, almost all of us can, say, run a marathon. Very few us of can run a marathon, however, at the pace that elite runners do. Even fewer could do so without undertaking very serious, elite-level, training to make the attempt. Similarly, while we can all talk, and most of us write, very, very few are realistic candidates for the best seller's lists, or Nobel prizes.
So it goes with science. Doing it at a professional level is a lot harder than doing it at all. One thing you often encounter in coming up with ideas is to discover that your wonderful, creative, idea was already thought of. I give myself points (when looking outside my field) for how recently it was thought of. More than 300 years ago, only 1 point. Less than 200 is more, and less than 100 even more. Every so often I manage to go out of field and come up with a new idea (to me) that professionals thought of only 30-50 years ago. On the rare occasion, I come up with one that they didn't come up with until within the last 30 years. I give myself a lot of points for those. They're pretty rare.
That's one part of doing science at a professional level -- your idea or discovery has to be not only new to you, but new to the world. Consequently, a lot of the training for becoming a professional involves learning what is already known. The answer is, unfortunately for we who'd like to make a grand splash of some kind, a lot. Worse, there are now centuries of very creative, knowledgeable people who have been working at it. Coming up with something novel is, therefore, hard.
A high school friend illustrated this neatly, if accidentally, for me. We met up over a holiday early in our college careers and he was complaining about the lack of creativity in computer science. For instance, thinking that something new and good was to be had by looking at 3 value logic systems rather than 2 value as was expressed in binary computers. He was confident such an idea would never be looked at. The week before, I was at a presentation about 3 value logic circuits and why they'd be useful. And the novel part was not the idea, which was much older, but how the speaker planned to implement it in hardware.
Conversely, if you'd like to do something novel, you're much better off looking at some area that is new, using new equipment, etc., so hasn't had a long history for people to work out a large number of ideas. In that vein, it's much easier to pull off on the satellite remote sensing of tropospheric temperatures for climate (a topic less than 20 years old) than for the surface thermometer record (well over 100 years old). A fellow I know published in the prestigious Geophysical Research Letters, largely on the strength of this point. Paper came out in 2003. He looked at how the Spencer and Christy satellite algorithm worked, and realized that it assumed something which in high latitudes was not a good assumption. He then worked out what the implications were (i.e., the trends in sea ice cover would be falsely reported as trends in temperatures), and documented it well enough to be published in the professional literature:
Swanson R. E., Evidence of possible sea-ice influence on Microwave Sounding Unit tropospheric temperature trends in polar regions, Geophys. Res. Lett., 30 (20), 2040, doi:10.1029/2003GL017938, 2003. (You can follow this up at http://www.agu.org/)
Now, the thing is, Richard did not have a doctorate. He had a master's. And his master's was not in science, it was engineering. What mattered is that he saw something that hadn't been noticed, documented it well, and submitted it to the professional publication. And he got published in this high profile journal even though he had no PhD, nor even previously worked in the field. I keep him in mind when people talk about the 'conspiracy to keep out' ... whoever.
On a different hand, as an undergraduate I did do work worth a coauthorship on a significant journal paper. (Significant journal, that is, whether the paper was significant, I leave to its readers.) But that was working for a faculty member, and while my contribution was indeed (I realized later, I assumed that Ed was simply a nice guy -- which he was, but that turned out to be a different matter) worthy of a coauthorship, I couldn't have gotten the project started on my own. Once started in a fruitful area, I could have finished it, but for a professional, you want to see the person be able to find out what the fruitful area is.
So how young can you go; how much experience is needed? Well, if you choose right, and are creative enough, jr. high. My niece managed a science fair project last year that I still encourage her to write up for serious publication. She hit on an idea in an area that hasn't been studied a lot already (it's new and people there have been assuming an answer, she documented it -- good science) and a way of testing it (ditto) and collected the data and evaluated it scientifically. Yay! She might need a hand on the professional writing and statistics description, but the science part, she nailed solo.
Where does that leave us as readers of blogs and such? Alas, it means we have to think. The presence of a PhD is not a guarantee of correctness. Nor is the absence of one a guarantee of error. And this remains true even if we consider what area the PhD was in and the like. What is more reliable is that the older an area (surface temperature record interpretation, for instance) the less likely it is that someone can make a contribution or correction without doing quite a lot of work. The field is long past the point where it's likely that they've not noticed the urban heat island, for instance. (I haven't searched seriously, but have already run across reference to it from the early 1950s.) Blog commentators who plop this one down as if it were an ace of trump: "Ha, they didn't consider the urban heat island. Therefore, I can conclude whatever I want." or the like, can speedily be added to your list of unreliable sources. Urban heat island has been considered, quite often, for longer than they've been alive. It's an old field. Tackling ARGO buoys, less overwhelming an obstacle. (But be sure your math is up to the work! )
As younger people (those of you who are, which doesn't seem to be many, alas; but you parents remember it for your kids' sake) it means that the time to start working on doing science is today. Do your own science (meaning, learn things about the world), and try to do some professional level science too (try to learn things that nobody else has figured out yet). The heart of science is in finding things out. This doesn't have to have anything to do with what you're doing in school. But things that interest you, whatever that may be.