Accidental Deletion
Deleting a file doesn't erase it. This is one of the more recoverable situations in data recovery — provided you act quickly and don't do anything else with the drive.
What's actually happening
When a file is deleted — even "permanently," bypassing the Recycle Bin or Trash — the file system normally marks its space as available and updates or removes metadata that referenced the file. The exact metadata changes differ between NTFS, APFS, ext4 and other file systems. On conventional magnetic storage, the old file content may remain readable in those sectors until they are reused; whether the original name, path and allocation information survive is a separate question.
How recoverable this really is
Two things determine how this goes, and neither has much to do with which software gets used. First, the drive hasn't been used for much of anything since the deletion — every write, even something as small as the OS updating a log file in the background, is a chance the freed space gets overwritten. Second, the storage type behaves the way this explanation assumes: a conventional hard drive, or an SSD with TRIM disabled.
SSDs need a separate warning. If the operating system issues TRIM/deallocation and that command reaches the SSD, the old logical blocks may stop returning their previous contents even before the underlying flash is physically erased. That makes deleted-file recovery much less predictable than on a hard drive; see SSD deletion and TRIM for the storage-stack details.
The general approach
Recovery software scans the file system's own structures for the traces a deleted file leaves behind — orphaned directory entries that still describe where the data begins, essentially a pointer nobody's using anymore. When even those are gone, tools fall back to scanning the raw disk for the recognizable byte patterns that mark the start of common file types (a technique usually called "carving"). The first method is faster and keeps original names and folder structure; carving works even on a badly damaged file system, but it typically can't recover names, and it struggles with files that were fragmented across the disk.
Don't keep using the drive the files were on — installing a recovery tool onto it, saving recovered files back onto it, or just continuing normal work. Any of those can silently overwrite the exact data being recovered. If the files matter, stop writing to that drive immediately, and do everything else — installing software, saving output — on a different drive.
For a plain deletion like this, a free tool such as Recuva or Disk Drill is usually enough to check whether the files are still recoverable — see the full directory of recovery software by vendor for more options, or free vs. paid recovery software for how to decide between them. A real backup, covered in Backup Drive Picks, makes this whole scenario a non-event instead of a scramble.
This page describes the general situation, not a guaranteed fix for your specific case. If you'd rather have someone experienced take a look before you try anything, see what a hands-on evaluation looks like.