Past tense after 'by'

I always see sentences like 'by było lepiej' or something of the sort...should that be translated into present tense, like 'in order to be better' or something? Can someone explain this?=)

Yes, it relates to the future but is said now so "in order to be better [in the future]" makes most sense to me.

There is actually a pretty close English equivalent:

'bybyło (past tense) lepiej' - "so that it were (past tense) better"

Grammatically speaking, “...so that it were better” is conjunctive, not past tense.

Though, in contemporary spoken English, you would hear “so it would / it’d be better” or “so it was better”.