Learn Italian: Nel rimuginare sul passato perdi solo tempo. - By brooding over the past you just waste time.

You could say Nel rimuginare sul passato non fai altro che perdere tempo. This literally means "By brooding over the past, you do nothing but waste time," which captures the exact same exclusive idea as perdi solo tempo.

Why is nel used directly before the infinitive verb rimuginare?

In Italian, using the articulated preposition nel (in + il) followed by an infinitive is a common way to translate the English "by doing" or "in doing" something. You could also express this exact same idea by using the gerund form instead: Rimuginando sul passato, perdi solo tempo.

Does the verb rimuginare always require the preposition su?

Yes, when you want to specify what you are dwelling on or overthinking, rimuginare (which shares roots with the English "to ruminate") always takes the preposition su. Here, it combines with the definite article il to become sul passato.

Could I place solo at the beginning of the clause, saying solo perdi tempo?

While you might occasionally hear that in very casual speech, the standard and most natural placement for an adverb of limitation like solo is immediately after the conjugated verb it modifies, giving us perdi solo tempo.