By remediation, I think that you mean transforming the lead into a less toxic or inert form. However, there are many ways that are being used to deal with lead and this is a very intensive and lengthy subject (books are written about it). Unfortunately, for the time being, the more common methods for dealing with lead is to bury it or cover it with top soil, or remove (excavate) the lead soil and move it to a landfill or designated holding facility. Also it is common to mix the contaminated soil with portland cement (binder) before transferring it to a landfill or elsewhere. Having lead extracted is kind of uncommon (still in the more experimental phases), unless the level is extremely high (and something must be done).
Transforming lead involves one or more of three strategies: thermal, biological, and/or chemical.
Thermal: Incineration (burning) contaminanted soil in either solid, liquid, or sludge form. Incinerator types- fluidized-bed incinerator, multiple-hearth furnace, rotary kiln, and liquid-injection incinerator. Air pollution is a potential problem for hazardous-waste incineration. For remediation of vaporized lead a filter/scrubber would be used to collect the lead.
Biological/bioremediation: Plants or microbes that can metabolize the lead may be added to soil, along with nutrients. With phytoremediation, lead is taken up (absorbed) by the plants... so the concentration of lead is higher in the plant, so the lead is easier and more efficiently extracted or disposed of. See more about phytoremediation. Genetically engineered species of plants are being studied. Microbes are not currently used for practical lead remediation, but that is likely to change (perhaps with the aid of genetic engineering). Heavy metal remediation using bacteria and/or fungi would be used to concentrate or change the form of lead for improved solubility/extraction.
Chemical: Technically, chemical methods only include ion exchange, precipitation, redox reactions, and acid/base neutralization, while the "physical" methods are sedimentation, flotation, and filtration. But the distinction between these sciences at this juncture seems more nominal to me. Also, phosphate stabilization is a chemical alternative, where phosphate is added to soil to bind up the metals (in the soil) so they are not absorbed into the body when swallowed. This method depends on the phosphate reacting/binding with the lead in the soil. EPA allows this (on a case dependent basis), but at the same time, heavily restricts the use of phosphate fertilizer because of pollution problems assosiated with phosphates (like algal blooms).
Edit- What precautions should I take (assuming that I do have lead) that will reduce or eliminate exposure to my kids?
EPA says, "if you plan on gardening in areas with lead and cadmium
- Consider a raised garden bed. This should be accomplished by
bringing in soil you know is not contaminated.
- Thoroughly wash all vegetables and peel root vegetables.
- Limit exposure to young children to contaminated garden soil.
- Avoid transporting contaminated garden soil into the home on shoes,
clothing, and pets."
Edit2: See also 5 Best Plants For Phytoremediation listed below:
- Indian mustard (Brassica juncea L.)
- Willow (Salix species)
- Poplar tree (Populus deltoides)
- Indian grass (Sorghastrum nutans) (Sorghastrum nutans (L.) Nash)
- Sunflower (Helianthus Annuus L.) (Helianthus annuus L. common