Hello, jphyde,
I’m going to make a few assumptions, but ask you to confirm that they are correct.
First, I am going to assume that the site has not had the login page obscured, so you would be able to add /wp-admin/ to the URL and be presented with a login screen, much like the one you used to log in to this forum. At that point, you will enter the username and password that the client gave you and you will then be directed to the admin view of the site.
Next, I am going to assume that the Blog post type has not been changed to something else, so you should see it on the left-hand side navigation. There will be an icon that looks like a pushpin.
My third assumption is that there is a page in the page list called Blog, or maybe Sample Page, or some other page that is not being actively used on the site. If not, you can create a new page and call it Blog. Next, you will use the Customizer to tell the theme that the page called Blog is the archive page for all of the blog posts. This is where the excerpts of the posts are listed. Scroll down until you see Appearance. Hover over that and click on Customizer. The Customizer will open on the left side along with a view of the website. Find the Home Page Settings. In there you will tell the theme that the Posts Page is the page called Blog. Click Publish at the top and exit the Customizer.
Now to add or edit a post click on Blog in the left navigation panel. You should see one or two sample posts which you can delete. Click Add New at either the top or left of the screen and a fresh new editing window will be presented. Create your post here and when you are all done, click Publish on the right side. If you wish to come back to a post and edit it later, click on Blog, then click on the title of the post in the post list to open the editor. Once the changes are made be sure to click Update on the right-side panel.
