From what I have gathered it seems a lot of students really need a confidence boost. Once they realize they are capable to doing well, they tend to improve their performance.
There is also like tricks and gimmicks, but that is a different discussion.
What did help is that I was encouraged to read a lot from a young age, which seems fairly accessible to most families.
Support your local libraries.
One bit of knowledge improved my ACT score from 27 to a 33: internalizing how long I have for the tests. I was so used to being able to finish school tests with a comfortable amount of time remaining, so I took the test at a casual pace which means I didn't finish. The second time, I sprinted through the test as fast as possible and my score improved dramatically.
I doubt I could have done better with more coaching or prep.
To me, those test prep places always seemed to be struggling with legitimacy. It's not like hiring a tutor to help you learn difficult concepts for the first time.
... which is part of why having parents who have themselves succeeded at these things is an advantage. Mine were from poor (quite poor, in one case) backgrounds but were worked-hard-and-eventually-did-OK sorts, not early-success sorts. So they taught me fairness and honesty in all things, and didn't know they should clue me in that some things are just bullshit games that you should do whatever you can to beat short of taking too-large risks. I mean, they hadn't even played most of those games, so how could they know?
I bet it would never occur to kids from an upper-middle-class background (doctor parents, lawyer parents, business exec parents, that kind of thing) that test prep is a bit dirty. Wouldn't even cross their minds. It's just what you do, obviously.