When it reads wrong

Read the screen first

Almost every problem with this board shows up on the serial monitor as one of a handful of patterns, and each pattern points at one cause. Pick what you see:

The three faults

No SC7A20 at 0x19 means the check in setup() failed: nothing answered, or something answered with the wrong name. In that order: GND, then SDA and SCL swapped, then 3V3 on a pin that is actually powered. The power light proves only the last of those.

Every axis reads 0.000, or the same numbers never change, means the chip is still asleep. CTRL_REG1 was never written, or was written with a zero data rate. The first sketch writes it in setup(); a sketch of your own that forgot it reads a chip that has never taken a measurement. It wakes up asleep.

A library says there is no chip when a scan finds one at 0x19. The library was written for a different chip and is checking the wrong address and the wrong name. Nothing is broken; the library does not know this part.

The two that are not faults

Level, but X or Y reads 0.05 or 0.08. The zero-g offset of a mounted chip is typically 90 mg and at most 120. It is not noise and it will not average away, but it is the same every time, so measure it once and subtract it. From counts to g covers it.

Z reads −1. The board is upside down, chip side facing the table. An axis reads +1 g pointing up and −1 g pointing down, and on this board Z comes out of the chip side.

And one that is waiting to happen

If this board is fed from 5 V, or wired straight to a 5 V Uno's pins, it may well work for now. The chip's absolute maximum is 3.6 V on its supply and 3.6 V on its pins at a 3.3 V supply, and a part run past its absolute maximum fails when it fails, not when it is wired. Feed it 3.3 V, and put a TK97 between it and an Uno.