How do I approach doing market research?

It's great that you have an idea ! If you don't know where to start, I'd say the best way to look at it is doing the following:

• The easiest way to do market research is through good old google searches. Look for the biggest trends in your idea's industry. You should get a feel for high level stats on the potential of the idea, i.e. how many people it could impact, what the total value of the industry is, if there's a huge gap in the market, etc. The more specific your idea is, the more detailed you can get with your trends
• Get an understanding of your competition, aka who else is offering either a similar product or a supplemental product? Super random example, but if you want to build a new calculator, you should know that your competition is current producers of calculators but it can also be other programs like excel, your phone, and the super basic pencil + paper. Doing this will give you a sense of who's similar / not similar to your product and how you can differentiate (or in some cases, maybe there's something you really like that you'd like to emulate)
• If you want to talk to people in your target market, the best way to start is having qualitative conversations. Try and find someone you'd go after and understand their problems, goals, etc. and then chat with them about your idea. They'll give you a lot of good insights to help you understand whether 1) this is a problem for them and 2) your solution would help solve it for them. You can go into these as simply conversations and still get a lot of great feedback on your idea without having to build anything.
• As for surveying, I'd only get into that once you know what you need to know.. A lot of times you won't know what you want to ask until you do some of the above
  Also, not to plug - but if you wanna learn more about writing surveys, I'm co-writing a few articles for people that want to write them but don't know much about survey design! You can find the first article on indie hackers here!: https://www.indiehackers.com/article/5ec001d986

Hope that's a little bit helpful :)

Who is your idea for? There are lots of ways online to gather initial market insights, but it depends a lot on your intended audience.

Generally surveys are less informative that conversations in the early stages, but they can be useful if you want to get some larger numbers on specific research questions.

Good that you are starting with market research :)