"I need to read a book."
Translation:Yo necesito leer un libro.
You're right! In your sentence the pronoun "Yo" can be omitted , since it's implied in the conjugation of the verb. "Necesito" can only be used with "Yo", so, no need to say it/write it. Most of the time, spanish speakers ommit pronouns in the sentences, like: "¿Qué quieres? (tú)", "(Ella) Es muy bonita". Of course, you have to be in context with the conversation or reading.
People get confused because, from the previous lessons they would have made a pattern that the verbs that end with 'o' comes after yo. Eg. Como, bebo etc.
But in case of Leo or Leer the difference is you need to use Leer when if you need to use the infinitive form (to read). Eg. "Yo leo" is correct, which means "I read". But for I need to read. Because of the 'to' invifitive, you need to use leer. So it's, "yo necesito leer".