Locating
One of these should be set up for you. Here's where you find your blog home page:
Then click Blog Home Page and you're ready to edit.
Editing
Now that you found it, you can set a title, meta description, and meta keywords, which work as described here in the context of content pages. Note that these fields only apply to the blog home page, as individual blog post pages have their own title, description, and keywords fields.
The only other field of the blog home page is Content, which is displayed above the blog posts. This comes with placeholder text that you probably want to replace with your own introductory paragraph.
When you're done editing the post, click the Save button as usual.
Removing the Search Bar
If you want your blog home page to not include the search bar, include the following snippet in the <> Source Code of your Blog Home Page content box:
Then, hit the Save button to save this change.
Deleting
Generally, it's better to edit your blog home page instead of deleting it. If you definitely want to delete it, find the blog home page as described above. Then, scroll to the bottom and click the Delete link to the left of the Save button.
