The user avatar can be set using WordPress native Gravatar support or by using a plugin like WP User Avatar. Avatars appear next to the user name on sections like Author Box or the post comment section:
To use this option first you have to register with Gravatar:
After you login go to “My Gravatars” section and set up your avatar image, just press the “Add a new image” link and follow the required steps to add an image
Click on the Upload New button to select a new image:
Click on “Choose File” button, select the image you want to upload and press “Next”:
If the uploaded image is large and contains elements you don’t want to display on the avatar logo you can use the crop feature to select only the image desired section. After you set the crop selection press the “Crop and Finish!” button:
Chose the avatar rating, the significance of each rate is explained bellow:
You’re done with the Gravatar settings, the logo should appear next to your email:
To enable Gravatar on your website go to Settings -> Discussion, scroll down to the “Avatar” Section and select “Gravatar Logo” as a default avatar.
For more details you can check wordpress official gravatar documentation.
WP User Avatar
Install and activate the plugin, you can search for it in the Plugins -> Add new section:
Next go to Users -> Your Profile and set your avatar image
The rest of the users can do the same from their account settings.