Basically よみます means "to read" and よんでいます means "to be reading".
However, in Japanese, dipending on the context, よみます is used for present and future and よんでいます is used for the action "you are reading" and "you do habitually after starting doing that".
あした、この本をよみます。(Tomorrow, I'll read this book.)
きょう、この本をよみます。(Today, I'll read this book.)
いま、この本をよんでいます。(Now, I'm reading this book.) *after starting reading
まいにち、この本をよんでいます。(I read this book everyday.) *after starting reading
I hope this helps you.