How am I supposed to imagine these so-called multiple universes?

Answer

There are two aspects to the answer I want to give you. First about ‘other universes’ and then about ‘imagining’.

The first aspect is somewhat linguistic in nature. The universe is ‘all there is’, there is only one everything. What we are discovering now is that the world is even bigger, more diverse, richer,…, than we first thought, but as far as I know the word ‘everything’ is not used in the plural. Such ambiguities are not new. Less than a hundred years ago it became clear that the ‘nebulae’ in the sky are separate galaxies. Before, it was thought that our own galaxy was just about it, and then it was established (once more, after the Copernicus revolution) that the universe is much bigger than we thought. Then people spoke of ‘island universes’ to indicate those other galaxies. Since then we have realized that our universe is bigger than we first suspected (which is quite understandable by the way), but we are making the same mistake again.
The problem today is a bit more abstract than it was then, because it’s not so clear whether we can explore the possible unexplored territory of our universe, which immediately raises the question of whether there is any point in talking about it. The question starts with why the laws of physics are what they are, because purely mathematically it could have been otherwise. A possible answer is that there are different ways to have physics (and calling that different universes every time is the linguistic problem), where we now just live in the (piece of) universe where our laws apply. And then we’ve determined that the part of the universe where we live is one that expanded very quickly at the beginning (the ‘inflationary universe’), so it makes sense that we only see this part and the rest not.
And here come those new measurements, also from the European cosmological satellite Planck. It may be that the universe that we can observe is no longer completely homogeneous, and that we can still see that and in what way we are a piece of something that is so much less small than ourselves. So that is very exciting and intriguing, but – I also want to emphasize that – no break with the past of our science.

So aspect two is ‘how should I imagine it?’. To be clear: you don’t have to do anything. Let’s talk about that ‘proposing’. Whereby I – with apologies to the loyal readers – repeat myself, this is by the way my 700th answer on this site.
The discussion goes back to Plato and Aristotle. Plato saw the phenomena as a reflection of a more fundamental abstract reality, Aristotle began to realize that what we can know and think depends on our empirical possibilities. Today everyone knows that we are a product of the world, but few realize that this also means that we have to give up the ambition to completely objectify the system, in order to have the last word. Not only the atoms that make up us, but also the conceptual framework that we use in our so-called autonomous thinking, is indebted to the world that produced us.
Because if you ask how to imagine it, you implicitly extrapolate spatial impressions of our world as absolute concepts. And that is essentially circular reasoning.
But even more fundamental than the discussion between Plato and Aristotle, your question was answered in Genesis 2. The man who thinks he has the key to grasp the ultimate meanings does not know his place in the system, for he wants to be God himself, and that is not very wise.