Survey before and after
Elevations are recorded before work starts and again at the end, so the change is documented rather than described.
Leveling is the lifting part of the job: bringing a settled section of the house back up in controlled stages, as far as the structure will safely take, and holding it there.
Leveling is not a starting point, it is a decision made after a floor survey. Plenty of Arlington houses read half an inch out and are perfectly fine. What matters is how much, where and whether it is still changing.

The lift is the visible part, but most of the care goes into deciding how far to go and watching what happens upstairs while it happens.
Elevations are recorded before work starts and again at the end, so the change is documented rather than described.
The house comes up a little at a time across several points at once. Rushing a lift is how plaster, tile and window glass get damaged.
Doors, brick joints and sheetrock are checked as the lift progresses. Sometimes the right call is to stop short of full level.
Once the position is right, the load is transferred onto the piers or pads and the access is backfilled and tidied.
This is the question people rarely ask and should. An older house has settled into itself: the plaster, the cabinets and the roof have all adjusted to the current shape. Forcing it back to dead level can crack more than it fixes. A sensible scope aims for a stable, much-improved house rather than a perfect spirit-level reading, and the quote should say what target is being worked to.
How the lift is held up matters as much as the lift itself. Compare the two common approaches on our concrete versus steel piers page, and see pier installation for how depth is determined on site.
On a crawl space house the same work is done with shims and pads from underneath, described on the pier and beam page. For slabs, see slab foundation repair, or call about a floor survey first.
The size of the area being lifted, how many support points it needs, the pier type and the access. Interior work reached by tunneling costs more than perimeter work. Ask the provider to price it from the survey and put the scope in writing before anything is booked.
Some movement in finishes is normal when a house is lifted, and a careful crew keeps it to a minimum by going slowly and watching as they go. You should be told before work starts which finishes are most at risk and who is responsible for cosmetic repairs afterward.
Usually not for perimeter work on a slab. Interior piers, tunneling or extensive crawl space repair can mean parts of the house are out of use for a while. Ask the provider which rooms are affected and for how long as part of the quote.
Find out how far out the house actually is before deciding anything.