I've often heard the comment that much of science is asking good questions. That's true. I also heard often in school that there are no bad questions, which is reasonably correct also. But there can be quite a distance between not bad and good. I can't, however, remember anybody describing how to go about asking better questions. There are probably many different ways of improving, so, as usual, I invite comments.
An important part of a good question is, it will be clear that it has been answered. Start with the not-bad question "What's up with climate?" Maybe you answer talking about sea ice and polar bears. But I'm unsatisfied because what I wanted to hear about was global temperatures. So I ask the improved question "What's up with global temperatures?", and you answer talking about how the stratospheric temperatures have dropped and surface temperatures have risen lately. But I'm still unsatisfied, because I don't care about the stratosphere, and the surface temperatures I care about are the ocean's. So now I ask "What's up with ocean surface temperatures?", and you say 'not much', or, maybe, 'they've risen'. Again, I don't have an answer. You're doing your best, and being honest, but the questions just aren't strong enough.
A strong question is "How much has global mean sea surface temperature changed over the past 150 years, and what are the uncertainties in that number?" This, neither you, nor I, nor any random spectator will have any difficulty telling whether I've gotten an answer to my question. It'll be something like "risen by 0.5 C and 0.1 C standard error in that estimate". Whether 0.5 and 0.1 are correct, I don't know offhand. But, at this point, the question has an answer which is fill in the blank. We can then hit the literature (say IPCC Ch. 3 and the citations in that chapter) looking for it. If the question didn't have an answer waiting for us in the literature, we also know how to start doing our research -- look for data sources about ocean surface temperature, that are distributed over the globe, and which go back 150 years (or more, of course).
A different strong question is "Why is the sky blue?" No reason that young kids can't be asking strong questions. An answer to this question must adress why the sky is blue, as opposed to green. And a strong answer will tell you how blue it will be under different conditions. If, for instance, you have a high humidity and many aerosols, the sky tends towards white -- under the action of the same process which tells us that the sky (away from the sun) is very blue when the air is clean and dry. (Rayleigh scattering).
Questions that start "What about ...", "How about ...", "What's up with ..." are almost never strong questions. Strong questions usually start "How much ...", "How fast ...", "How big ...", or say "How well do we know ...".
If we really don't know much about an area, which is the case for us for most areas of human knowledge, it can be hard to ask strong questions. So we start with the not-bad questions aimed at learning more about the area, and keep asking them until we can ask strong questions. Hence my 'question place'.