Thank you for posting your blog with the Basement Health Association. You must start with a licensed engineer or an architect and contact your local building department regarding the necessary permits. Your search for a reliable contractor should include references on under-pinning projects that they have performed. This project will require an experienced crew to transfer the load of your house to a new section of foundation. Improperly executed under-pinning can result in structural damage. Based on your blog I would imagine you are trying to accomplish at least an 8 foot ceiling height. This would require adding an additional 24 inches of concrete to the bottom of your foundation in 4 -5 foot sections at a time. The costs for under-pinning usually run between 75 and 100 dollars per linear foot. Once the foundation has been under-pinned the crew will then begin to remove the 24 inches of soil. Excavation costs should be estimated at approximately $3 -5 dollars per sq. foot. The basement colums or supports will have to be changed to meet the new height, this will require temporarily supporting the floor joists, installing a new concrete column pad and a steel columns. New concrete colums should costs $1,500 dollars per column. Based on your location and ground water conditions this would be an opportune time to install an underfloor drainage system with an approximate cost of $60 -$75 dollars per linear foot. A vapor barier will be necessary prior to the installation of a concrete slab with a cost of aproximately $8.00 per sq. foot for concrete and a $600 dollar charge for a concrete pump. Please keep in mind it will be necessary to determine the actual depth of the ground water so there are no surprises in the middle of this project. Also, this type of work requires a company with experience with this type of project. Good Luck.