This is the easiest way to add "read more" in blogger. i just discovered it so i decided to show it to everybody because most of the sites i visits gave me long and hard way to get this feature. This is the easiest way to do it.
After write your article, click at the place you want to put Read more and just click on insert jump break look at the picture below to see it
click on edit html to see if you can see it in like in the picture below
After you finish, click publish post and view your blog and see if it work.