*Update* As of WordPress v5.0 WordPress has included a new post and page editor interface called 'Gutenberg'. If you prefer to continue using the classic editor that you're used to you will need to install the Classic Editor plugin and follow the instructions below.
From within your post or page, click the Add Media icon above the text editor box.
Browse on your computer to select an image and click 'Select Files' or drag and drop image to upload.
Review the Attachment Display Settings and click "Insert into Post".