How to Express Being in Early, Mid, Late of An Age Group
 

For example, how would one say I am in my early-mid-late 30s? Estoy en los principios de las 30? Los medios de las 30? Los finales de las 30?

Treinta y pico means in your thirties or thirty and then some.
Más o menos treinta means about thirty.

I don't think we make so many differences; we don't seem to care about how close we are to what "side" of the decade.
As Poli said, if we don't want to tell our age or want to guess someone's age, we'll normally say: "tengo treinta y tantos años"/"tiene unos treinta y tantos años".

Side note, when someone feels too old to avow their age, they may say "treinta y pocos" (for example), as a humorous way to mean they aren't too close to the next decade.

Same for the other decades: "veintitantos", "cuarenta y tantos", etc. That's always vague enough to avoid disclosing one's exact age.

Is it correct to say "Estoy en los treinta" to say I'm in my thirties?

I think that would be understood in context, but "en los + decade" is mostly used for a time in the century, like in "en los años treinta" (in the thirties).

:thinking: Yet, now that I think about it, I've heard something like "estoy en mis treintas", "un hombre maduro, en sus cincuentas". However, this is relatively new... due, I guess, to the influence of English. My aunts and grandmother probably would have found it very strange. :D