How can people evaluate scientific questions when they don't understand the science?

If we’re talking about a situation where a person is unable to understand the scientific argument sufficiently to make an informed judgement, then that appears to me to answer the question itself. No view.

If it is of such a nature that we must form a view, for instance a medical issue, then I’d be inclined to either trust an expert or get a couple of expert opinions and assess the risks if there is conflicting advice

The difficulty sometimes is that where a subject is contentious, there are opinions which are argued so confidently and effectively that it is hard for the lay person to decide between them.

My gut reaction is that there are probably lots of situations where expert advice conflicts, but I’d guess there are not very many where we can’t find enough information to form an opinion for ourselves.

I sometimes think that if a person cannot explain their view clearly enough for the lay person of average intelligence, then they probably don’t understand it very well themselves.

...when we are faced with a scientific question and we don't understand the scientific arguments about it, how should we decide what to believe? (Or should we decide not to believe anything?)

You might start by questioning why in the world one would need to rely solely on scientific argument in the first place.

Sometimes science is complex, not because of the basic concepts but because of the intricacies of the techniques used to arrive at theories. I'm thinking in particular about physics which is tied so intimately to mathematics. I may understand why the two slit experiment is so utterly counter-intuitive but not understand a single line of the mathematical notation that describes the outcome of the experiment. So you can have philosophers who understand the concepts - perhaps sometimes better than the scientists - without understanding the maths in the slightest. Which is why the greatest scientists have always been the philosopher scientists such as Einstein, Heisenberg, Shrödinger, etc. But it is also why there is a market for pop-science books so that the layman can have the ideas explained without the requirement for the nitty-gritty training.

Then there is the influence of biased thinking. Some scientists are not reticent about their faith in certain metaphysical positions, particularly materialism. Should we just ignore this and look at the letters after their names for reassurance that they must know some incontrovertible truth? I have no formal education to speak of but even I have heard some pretty dumb statements from the mouths of "experts". 

To quote Richard Lewontin who is one of those who proudly proclaims such a faith in materialism:

Our willingness to accept scientific claims that are against common sense is the key to an understanding of the real struggle between science and the supernatural. We take the side of science in spite of the patent absurdity of some of its constructs, in spite of its failure to fulfill many of its extravagant promises of health and life, in spite of the tolerance of the scientific community for unsubstantiated just-so stories, because we have a prior commitment, a commitment to materialism. It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door. The eminent Kant scholar Lewis Beck used to say that anyone who could believe in God could believe in anything. To appeal to an omnipotent deity is to allow that at any moment the regularities of nature may be ruptured, that miracles may happen.

You might start by questioning why in the world one would need to rely solely on scientific argument in the first place.

Actually, one of my options was included as an acknowledgment that some people preferred a non-scientific approach - "(5) We can proceed on the basis of intuition."

Perhaps I should also have added "revelation" and/or "faith".

Actually, one of my options was included as an acknowledgment that some people preferred a non-scientific approach - "(5) We can proceed on the basis of intuition."

Perhaps I should also have added "revelation" and/or "faith".

Are you saying that intuition is worthless?

Are you saying that intuition is worthless?

Well, in terms of the scientific method I don't think intuition can play any part in finally deciding what view to take (though of course it can play a big role in the "exploration" that leads up to that).

But I'm also acknowledging that for some people the scientific method isn't of primary importance anyway. There are alternative ways of looking at the world, and that's a matter of personal choice.

The only one of those suggestions in my original post that I think is completely worthless is the last one: "(6) We have just as much right to an opinion as anyone else, even if we don't understand the scientific arguments."