Google provides tools to measure LCP in a lab and in the field, including:
Search Console (field)
PageSpeed Insights (lab and field)
Web Vitals Extension (lab)
Chrome UX Report (field)
Chrome DevTools (lab)
When it comes to lab versus field data, both can be useful. Lab is important for testing and working on improving your scores. You will get a greater variance in results, but lab data provides instant feedback.
Field data is more important when you’re trying to get the overall view of your site. The values represented will depend a lot on your users’ environments, for example, mobile cork bicycle zone versus desktop, their internet speed, their computer performance, etc. The field data is nice because it gives you an idea of how your site is performing for everyone, not just how it performs for you.
To get started, Google provides a general roadmap for how to use the tools provided to diagnose a core web vital. Out of the following list, the first three are good. I would wrap up after the third bullet by saying to publish your changes and start seeing the benefits of increased performance. The remaining bullets (4th to 6th) are “nice to haves.” The last bullet likely won’t apply to 90% of websites.