Home lead testing kits

You have to actually eat, inhale, or otherwise take in lead paint for it to cause lead poisoning: it can't be absorbed through touch. So, if you find paint flaking anywhere, you should keep your children out of the room, scrape the flaking area (while wearing a mask), and repaint. Then clean the area thoroughly, especially if flecks fell on anything they are likely to stick in their mouths.

Be wary of lead paint on surfaces that may become scraped/worn easily, as that could lead to lead paint fleck/powder flying around.

If you still feel concerned, you can have the house tested. Also, be aware that US public schools are required by law to offer free lead testing in kindergarten and first grade.

Thanks to Robert for suggesting this link from the EPA on lead hazards.

Stop sanding immediately! Lead based dust is the worst threat of all. Simply painting over it to encapsulate it is the simplest measure.

To fully remove the lead paint is a big chore, and important to do right. Look for local community classes if you can - the local one here had some classes on lead certification. The short answer is, you have to seal the area off with plastic, wear a hazmat suit, scrape it all off and remove the paint from the premise, and then clean up all the dust.

You can google around and turn up tons of hits for lead removal procedures, here's the first I found and looks pretty good:

http://www.health.state.mn.us/divs/eh/lead/homes/interior.html

One tool I used in my own lead paint removal was http://www.speedheater.us/

While it is stated not to use heat guns to remove lead paint, this one is a much lower temperature version that is much safer. The fumes are still an issue so make sure there is ventilation to outside while working. (Not related to speed heater, just a happy customer)