Make sure the soap and surface dust is removed. Then apply latex concrete floor paint.

Try renting a carpet cleaner (get the large one if you have a big basement) at Home Depot or Lowe's. Use hot water and the liquid detergent in the bin and work the floor twice - once north to south and once east to west.
I used the cleaner machine after I moved into my new home and got a lot of dirt up.

If it's bare concrete, that may be the source of the dust....if so, you can't really wash it all away, since it is coming from the concrete!

Alex

DON"T do it now! If it is a newly built house you need to allow the concrete to fully cure. Also time will allow the house to settle and you can see what hairline cracks are going to occur.

Yup, you have to wait.

If the kids are playing down there, might want to put a cheap area rug down for a while. A year or so later, go ahead and clean & paint.

Using latex paint, I've not found any reason to wait in the last 20 years of building new homes.

A month or two of curing is all that's needed.

Keep in mind that by the time you get your new home, the basement floor may be as much as a year old.

Here is a link that might be useful: Concrete Painting

Yeah, it's been close to a year since it was poured... I've never heard you have to wait, but since it's that long anyway, probably not an issue. Thanks for all the comments so far!

Go ahead and paint it now. It will be OK.

Good Luck, The PorchGuy

Here is a link that might be useful: My Album