If you have a power tool surface that's absolutely flat in some dimension, that's good to use. If you have a bench that's very flat, then finding something supplemental to use on it is a good idea.

I have always used an 8x42x1/2 inch piece of glass on a flat bench surface. I use Mirka gold (doesn't matter the brand) aluminum oxide PSA stick down paper. PSA is important, as any paper that is not stuck down will dub the toe and tail of the plane in question. It won't render it unusable, but there's no reason for such ugliness, and the PSA paper can be used in push and pull directions.

That's pretty much it. Use the plane with the blade retracted and push the plane with the handles or with a hand between the handle and frog, as if you were using it. No wailing around is needed. If we are talking about a long jointer, sometimes it's easier to take a small block, say 2x3 and use 60 grit paper to do bulk removal of metal before final lapping, but I have also lapped #7s in a half hour or so on good fresh 80 grit al-ox paper/rolls.

Less is more lapping planes - get things as flat as they need to be and then stop.