How can I translate "Read More" on Drupal 7
Assuming you have added and enabled another language in admin/config/regional/language

Just head over to admin/config/regional/translate and search for the string you want translated.

IMPORTANT The strings are both case and whitespace sensitive. Searching for "Read More" returns no results but "read more" has a hit (see screenshot).

Also, since a lot of strings have placeholders that are substituted with variables you might have better luck with other strings if you search for a small subset of it as opposed to the entire thing!

Additionally, I strongly recommend installing the Localization Update module, it will automatically download and update translations for all contributed modules.