With the little information given and the asker's obvious lack of understanding about hard drive technology, the obvious answer would be to contact a data retrieval service and let professionals deal with the problem before the drive fails entirely and data retrieval becomes even more expensive to the point where it isn't an option any more.
Hindsight: You should have copied off all the data when the drive was still recognized by the system. Any damage that the fall may have introduced could be increased by using the drive, so you should have used this opportunity to save your data. It would have been a good idea to ask first before exposing the drive to the excess stress of using a repair software. This doesn't help you at this point, but it might help other people who come across this question.
There are a few ways that could allow you to access the data depending on the physical damage that has been done. Needless to say, this drive is done for and any method that might revive it will not be enough to repair it, but is solely mentioned as a way to get data off of it.
Damaged logic board
If the hard drive's logic board has been damaged then this could lead to the drive not being recognized or function at all. Depending on the make and model this might be more or less likely after a fall. You'd need to have to track down the exact same model and build and replace the board with that of the replacement drive. Granted that all the mechanics are okay, this would allow you to get this drive to be recognized again, allowing you to backup your data.
Damaged init sectors
A hard drive contains sectors that carry information about its technical specs. If those are damaged, it cannot be properly initialized. To get around this problem, you'd need a secondary hard drive of the same model. You can use it to initialize itself and then switch the damaged drive in.
Remove the logic board from the damaged drive. Boot your system with the replacement drive. Once your operating system is running, you have to send the drive into standby mode, remove the circuit board from the drive while it is still attached to the computer. Now attach that logic board to the failed drive. Since the replacement drive has already been initialized, you'll then should get access to the rest of the drive once you wake it up again. This may or may not work with every drive and an external SATA adaptor is recommended so that you can perform the switch on your desk.
This is most likely the case after a fall. The reading head might have been bent out of shape. Heads may have scratched the surface, or the motor may have failed. There are ways to replace all of them, but they not just require an identical hard drive, but also special tools, for example to make sure that the platter alignment isn't destroyed if the platters need to be transferred to the replacement drive and such. If the platters have been damaged then a repair might not be feasible unless even data fragments are of value to you. Needless to say, this should be done by experts.
Why NOT to freeze the hard drive
I'm appalled to see this suggestion a couple of times on here. It seems so simple yet effective, so why not try it, right? Let me explain where this myth is coming from. Decades ago hard drives used certain forms of lubricant on the platters. As the lubricant aged, it developed glue-like qualities preventing the drive to boot up. This was a well known shortcoming in the design of these old hard drives. Some people put those drives in the freezer so that the temperature difference and the resulting contraction of the lubricants would set it free again.
The method was used in the 80s and early 90s and had proponents and while it may have worked back then, the situation today has vastly changed. So no freezing of the hard drive will help with any of those problems described. Yet, this outdated "solution" is still being perpetuated today by those who have no idea how hard drives work or how an effect of cooling it down would be able to temporarily getting it to run again.
The above list is by no means complete and the methods were described to showcase the complexity of getting failed hard drives back to work. Don't waste your time and mess around with the hardware if you have no experience with it! Finding a replacement drive to perform these tasks can be a tough act alone, especially as drives get older. It would not be enough to get a second Buffalo Mini Station as those will house different drives depending on manufacturing dates and locations.
Should your system recognize your hard drive again then
- copy off your data, starting with the most important one!
- Do NOT use repair software on it! It intruduces extra wear and tear which may send your drive over the edge! This software is only useful for software errors, not physically damaged drives!
- If no data is readable then use imaging software and work on the image rather than directly with a drive that could fail any second.
I suggest you evaluate how important that data is to you. If it's replaceable then get a new hard drive and forget about the hassle of getting it back. If it's irreplaceable then contact a proper service to help you with data retrieval. Many services have a policy where you only pay if they manage to retrieve data. Keep in mind that any extra work you perform with or on this drive might decrease your chances for professional data retrieval and might increase the cost of success.