How can I recover lost data from a failed hard drive?
First make sure that drive is powering up , then try to open it with an linux distro , or you can use easeus recovery program ( it costs) , also check Oron's answer.
If the drive is recognizable but not booting - you can either put the drive in another working computer or use a USB to SATA/IDE (depending on the drive) cable and check it out on a working computer. I do this all the time for people. Be sure to scan for viruses (if that's the reason the machine stopped booting especially).
[Above Omron recommended an enclosure - which is fine but I use just the cable which is essentially the insides of the enclosure - because I use it for bare drives I'm pulling out of desktops/laptops all the time. Either would work fine.]
As the others have alluded if the drive is not recognizable then you are pretty much left to going to some expe$ive data recovery type place (they take the disks out in a clean room and put them in a working drive).
There also used to be a great program called GetDataBack. I used it a time or two as well (for a drive that was working - recognizable - but the file allocation tables were hosed up on). RECUVA works well on deleted files. I've used it a time or two also.
If the drive is not recognizable i am afraid no software can help you to recover data, You must search some data recovery firm around your place and take your drive to them. Data Recovery companies can recover lost data but will cost a bit too much.
Check Oron answers, if files are valuable for you then perhaps to check technician company help and this will cost
It depends on the nature of the failure. If it's file-system corruption, you can use software such as one of the packages listed at //www.makeuseof.com/tag/best-windows-software/ (I recommend Recuva in the first instance as it's very easy to use).
If the failure is of the actual hardware, then you may need to send it to a data recovery bureau, and be warned, it will cost a lot!
That said, if it's an external hard drive, and the fault is simply that it is not responding (or perhaps not powering up at all), you could try buying an external enclosure (they're not expensive, a few dollars for a 2.5" enclosure, and perhaps $20-30 for a 3.5" one) and transfer the hard drive from the old enclosure to the new one. With any luck, this will solve the problem. Note that if the problem is a grinding or clicking noise or a constantly flashing light, then it's the actual drive that's damaged and this will not help.