Hello alexprobb,
Thank you for your question on adding the Categories widget back to the blog. Without a specific theme, I will have to speak generally, but the method should be very close if not the same.
From your dashboard, hover over the ‘Customize’ option and select the ‘Widgets’ option.
When the Widget tab opens, look for the ‘Edit in Admin’ button and click it.
From the left-hand column of ‘Available Widgets’ drag the ‘Categories’ option to the appropriate area listed on the right. It is normally ‘Sidebar#1’ but this is where it may differ, depending on theme.
Kindest Regards,
Scott M