The Constitution requires just compensation for takings under eminent domain - usually interpreted as what a willing buyer would pay a willing seller.
For properties of low estimated value (below $50K?), the Government does not conduct a formal appraisal, and makes an offer based on their informed estimate. The owner can accept that settlement, negotiate with the Government reps, or go to court to sue for a higher payment. For a small home where the barrier will take the back 150 feet of the yard, the home owner might be offered a few thousand dollars.
Hundreds of such cases will have to be settled in the Rio Grande Valley for the new Trump barrier. Some cases have not yet been finalized from the Bush-era barrier program that ended in 2009.
From what I have heard reported, money has been budgeted to reasonably compensate land owners this time around, more so than during the Bush-era Secure Fence Act program. Lessons have been learned.
The gov knew how to do this in 1942—
From Wikipedia Oak Ridge TN article
Starting in October 1942, the United States Army Corps of Engineers began acquiring more than 60,000 acres (24,000 ha) in the Oak Ridge area for the United States’ Manhattan Project. Unlike the earlier land acquisitions by the Tennessee Valley Authority for Norris Dam—which were still fresh on the minds of many Anderson Countians—the Corps’ “declaration of taking” was much more swift and final. Many residents came home to find eviction notices tacked to their doors. Most were given six weeks to evacuate, although several had as little as two weeks. Some were forced out before they received compensation.