The SSD maintains a translation table for all the virtual addresses exposed by the drive, that maps to the underlying flash physical addresses. Any physical address not in that table, is unallocated and the drive can use freely.
With most SSDs, there's no special explicit step necessary to overprovision a device. Just trim/unmap/discard a range of logical block addresses, and then never touch them again. The drive won't have any live data to preserve for those LBAs after they've been wiped by the trip operation, and the total amount of live data it is tracking will stay well below the advertised capacity of the drive.
The easiest way to achieve this is to create a partition with no filesystem, and use blkdiscard or similar to trim the LBAs corresponding to that partition.
