WordPress uses a tool called the Customizer to allow you to change different parts of your theme. What is changeable depends on what the theme author allows to be changed. These include things like fonts, colors, images, menus, headers, footers, etc.

Some plugins affect what is available in the customizer. For example, I have a plugin on my website called Accessibility that uses the Customizer as a way to customize the appearance and location of the accessibility icon. This is not controlled by the theme and works the same regardless of the theme that I installed. 

Draft Customizer Screencast

Customizing Menus

Draft Editing Menus Screencast

Menu customization can happen in two places - either through the customizer or through the original menu editor. If your theme allows menu changes through the customizer, I recommend using that method. You can select any page, category, or tag to be a menu item, as well as links to specific web pages. You can also change the title of the meny. Generally you want your menu to have short titles.

Further, your theme may allow for multiple menus and they may be located in different places. The various features depend on what the theme author has created. Before creating your menu, consider web design better practices that include having your logo go to your home page (most themes do this automatically now), having your About menu on the left edge of your menu and your Contact on the right edge.

Menus have names/identifiers and they have locations. The name/identifier can be anything you want it to be; however, the default names are primary and secondary. The location is determined by your theme and includes locations such as: header, footer, sidebar. The location options for your menus depend upon your theme.

Adding Widgets

Draft Widgets Screencast

Traditionally, widgets were used to add dynamic content to your website. Now, widgets are areas of your site where your theme allows you to add various blocks. In most modern themes, you will have several widget areas. You can add anything that is available within a block. One example of where widgets are used is on the sidebar. If your page has a sidebar, the content of that sidebar is added using widgets.

Adding Custom CSS

Sometimes you want to change something specific and your theme does not allow that customization. You can use CSS to create custom formats or to modify existing formats. 

Draft Editing CSS Screencast