To open the Developer Tools, right click your mouse (on desktop) and select Inspect from the context menu.
The Elements tab of the Developer Tools (Inspector tab on Firefox) lets you explore the computed HTML structure of the current page of your website.
This view is particularly useful for debugging your layout and finding problem elements.
The Network tab shows you all the individual requests which have been made on the page. This includes requests for CSS and JavaScript files.
This view is particularly useful for finding and singling out an image which may otherwise be difficult to target using the Elements tab view.
Other useful views include the Application/Storage tab which shows local storage data, including cookies, and of course, the Console which provides an interface for interacting with the website using JavaScript and is useful for logging messages and detecting errors.