To get a basic view of science, go to educational websites aimed at school pupils studying science subjects. In fact I have found a good starting point for research into practically any subject is to look at materials written for children. I have often used BBC Bitesize to get an introduction to subjects I know little about.
If you want something a little more advanced, search for books, magazines or websites about popular science.
You might also consider going on an evening course if one is available near you.
The trouble with anti-gravity and so on is that such things are far beyond the level of present day science. I am usually a strong proponent of researching from facts, not from fiction, but in this case fiction and speculation is all you've got! So try reading science fiction novels by well known writers dealing with the pseudo-scientific topics you want to cover, not to copy them, obviously, but to get a sense of what is considered plausible and what jargon to use.
The Wikipedia pages on mainstream scientific topics are usually accurate, but pitched at an intimidatingly high level. In contrast the Wikipedia pages for "far out" topics like anti-gravity are fairly readable and don't have a lot of mathematics.
I am a native English speaker, but often prefer the Simple English Wikipedia to the standard Wikipedia for research.
I would also recommend an old (1983) but still useful book called The Science in Science Fiction edited by Peter Nicholls. The chapters on biology and cloning have been mostly overtaken by scientific progress since then, but the parts dealing with speculative technologies of the far future obviously haven't been. Chapter 4 "The Limits of the Possible" has a section on anti-gravity.
Added later: as you state in your question, your aim here is to get enough of a grounding in science to come up with convincing justifications for futuristic technology. Better understanding of scientific principles will definitely give a more authentic flavour to your science fiction, and will also help you think up new ideas, but remember the writers' proverb that research should be like an iceberg: only 10% of it should be visible on the surface. Remember that to your characters flying cities will be mundane. They will not feel the need to explain them to each other.