I have just purchased a house and it has a concrete floor in the
basement. When we had the house inspected our inspector said it was
from water coming through. The floor is not level, meaning it has high
spots and is soft under the linoleum tile that was laid over it. I
would like to grind off a few inches and poor it again.
Has anybody done this or have any helpful hints.

When we had the house inspected our inspector said it was
from water coming through

What was from water coming through? Mold?

I would like to grind off a few inches and poor it again

Instead of grinding you can pour self-leveling compound which is pretty
easy if you know how to mix a bag of powder with the specified amount
of water. But if your basement is big that can get quite expensive at
$28 per bag, which only covers 1/8" over 50 sq. ft., or 1" over 6.25
sq. ft. I think it is mostly portland cement in the bag.

Maybe try a local concrete dealer for pricing or hire someone to do it.