This post combines my notes from master keyword research by Nick Eubanks and some of my process for doing keyword research.
When performing keyword research for an existing website, it's best to leverage existing data that will tell you what keywords the site is currently ranking for.
1. Use Google Keyword planner
In Google keyword planner > Search for new keyword and ad group ideas > Enter the website into Your landing page field > Turn on only show ideas closely related to my search terms and Google will show you a list of search terms related to the site.
2. Use Google Analytics
The Prerequisite for this is you have to integrate your google search console with your google analytics account. Once done, in Google Analytics > Acquisition > Search console > Queries, you will find a list of keywords that are driving traffic to your site. You can then slice and dice this information and create custom report with the rest of Google analytics data available to you.
3. Use Google search console (GSC).
If you're not using google search console, you're missing out. GSC offers a wealth of insights on your website/webpages', CTR, keywords they're ranking for, its rankings and more.
Once you've compiled a list of keywords from all these sources, you'll be able to map out where you stand in your niche and identify keyword opportunities you can put more effort on.