"I don't read a lot."
Translation:Yo no leo mucho.
I think in this case it has to be leo because its still you doing (or not doing) the verb leer. I dont read = Yo no leo.
I guess that, in the right context, "(Yo) no leo
muchos" is also a possible translation, where "muchos" would refer back to something just mentioned and the English "a lot" would be equivalent to "many".
No leo muchos pero los pocos que he leído son muy buenos.
No leo muchos pero me gustan mucho'... [followed by a list]
Leer = to read (infinitive form). LWP = ( I ) read (in Spanish you don't always have to specify the person/ subject.
"tantos" would mean "so many" or "as many" and would be referring to something already mentioned eg
Sueles leer artículos científicos sobre cosas relacionadas con lo que estás estudiando?
La verdad es que
no leo tantoscomo debería
ie "I don't read as many as I should".