Know the state of the art
I believe that there are no real shortcuts except in actually knowing what is the state of the art in the field, what approaches have been tried, what is being used right now, what is not being used because it's been tried in 1980s and doesn't work, what's happening right now, etc. A thorough literature search for keywords relevant to the topic, as some other answers suggest, is a necessary, but not sufficient part of that.
In addition to that, you'd need to follow up all the related approaches, perhaps try them out experimentally (depending on the field), look up if similar things have been tried for all the many, many other problems that are somewhat similar, browse the abstracts for all or most papers in journals or conferences in a subfield to see what other solutions have been tried, etc. It's not "how to do it efficiently/quickly" for a particular paper or solution - it's about doing lots and lots and lots of inefficient work to obtain lots and lots and lots of background knowledge as a table stakes of starting serious independent work in a particular subfield of science, which will then help you (and others!) for many papers in future.
I consider that researchers entering a field are expected to obtain that expertise (or most of it) during their PhD program, and that state is something that can take at least two or more years of full time work to obtain initially (i.e. it's not something that is plausible to have for your first paper in a field) and it deteriorates quickly, needing many hours each month to keep up.
Ask people who know
Of course, it's impossible for everyone to know the state of the art for every field; and it's impossible for anyone to know the state of the art in "their" field if they're just starting. But as I said, I believe that there are no real shortcuts, except asking people who do know that. If you can't do proper independent science in a field yet, then that doesn't mean that you should be doing improper science. It means that you should be doing science that's not fully independent. In particular:
- If you are doing a PhD in that field, then your advisor should be someone who knows that field. If it's not, you're going to have a hard time because you'll need to put in more work to get that knowledge yourself as soon as possible
- If your research leads into another field, then it's really, really helpful to involve another researcher from that field. Interdisciplinary research is great, but barging in some field 'uninvited' and uninformed is not going to win you any favors - get a co-author to review your ideas and provide insights from that field, and it's going to be a win-win.
- If you're experienced, and it's "your" field, and you still don't feel secure about what is original and what isn't, then you need to spend more time on reading semi-related research of others in order to keep up to date. There may be all kinds of conflicting time pressures from teaching or project work or whatever, but that's what needs to be done.
I'm aware that it's a big burden, and especially in some fast moving fields there's a real "Red Queen's race" and it takes all the running you can do to keep in the same place - but if it takes 10 hours a week of skimming papers every week to keep up with what's happening in your field, then that's what it takes to do proper research.
If someone is devoting, for example, just 20% of their working hours to science because of non-science academic duties or because they're working in industry, then that implies (at least to me) that they won't be able to do independent contributions to the subfield because that time is barely sufficient to keep up with what's the state of the art in that field, and knowing what is novel and what has been tried requires involving someone who is arms-deep in that field full-time or close to that.
It doesn't necessarily mean someone more senior - I have seen full professors who fully rely on a particular post-doc or PhD student to be up to date with all the literature on some particular topic.
I'm sorry if it looks like a rant, but to summarize I really want to make the following points:
- a short-cut way to do it 'efficiently' seems implausible;
- 'Ask people' and 'Talk to your supervisor' are good short-term solutions, but in the long term the goal is (or should be) to shift from 'ask people' to 'become (for your topic) the person who gets asked'. It's a lot of work, years of work, but it needs to be done.