This code snippet will allow you to customize the “read more” link when you have either “display post content” or “display post excerpts” set for content archives. It also works when manually inserting a “read more” link in a post.
Additionally, if you would like to style the link to look like a standard button, here is some example code to work into your style.css file. This particular code will make the “read more” link consistent with standard button class used throughout site. It also centers the button and reduces the width. Will likely need to be adjusted to fit your theme.