There are basically three ways of reporting an issue depending on your browser.
The webcompat report form is the main avenue to report an issue.
Webcompat.com Reporter for Firefox (normal and beta releases)
Webcompat.com Reporter for Chrome
We do not have currently an extension for Chrome on Android and Safari on iOS, you are welcome to contribute to the project, see Support reporting issues from iOS browsers and Chrome for Android.
For now, only Firefox Nightly and Firefox Developer Edition have a feature for reporting issues directly from the browser interface.
On Firefox Desktop, there is a ••• menu with a Report Site Issue option in the URL bar. Once selected, it automatically brings you to the webcompat reporting form with pre-filed data about your configuration.
On Firefox Android, you can use the menu button and scroll down to the Report Site Issue option.
Other browser vendors are welcome to provide a way to automatically report issues to webcompat.com in a similar fashion in their pre-release versions. Open an issue on the webcompat.com project.