Basic theory of file recovery
There seem to be more than one problems and questions asked here. I’ll restrict myself to the recovery of deleted files, after the recycle bin has been emptied. This is the theoretical answer, given not as help but for academic knowledge.
For easy cases, there are freeware tools that will do the job. The less you have used the computer in the meantime, the higher the chance of success.
For tougher cases, there are premium tools that get results at a price. A good one has already been mentioned.
For really difficult cases, where the HD may be damaged, there are professional labs that can reconstruct the files. But that’s very expensive.
Finally, it is not widely known, and may not sound believable, but even if files have been destroyed by shredding or after the disk has been reformatted, there are still means of recovery. But you may need the CIA to achieve that.
In theory, the only way you can be sure that files cannot be recovered, is to smash the HD to pieces with a sledgehammer.