The absence of a hard drive on your system can have multiple reasons of which I want to discuss the most common here:
If it's a new hard drive or one that you have just plugged into that specific machine, you might want to check if the cabling is correct and, in case it's an external one, if it has a power switch hidden somewhere on the back.
One other thing with new hard drives is that they are not formatted but have only "unallocated space" on them. This is most likely the case if your new drive is recognized by the BIOS and your device manager but doesn't show up anyway. To check this, have a look at the device manager - you can find it by going to Control Panel > Hardware and Sound > Device Manager:
In the screenshot above you see my Seagate disk drive displayed. If you're not sure whether what is shown there really is the drive you've plugged in just search the internet for the cryptic name you have in there. If the new missing drive can be found here you most likely only need to format it (do that only to new drives that have no data on them - formatting will cause a complete loss of data on a populated drive). To do that Windows has a tool called Disk Management which you can find in Control Panel > System and Security > Administrative Tools > Create and format hard disk partitions:
A new disk has none of those fancy partition blocks with colored stripes yet but plenty of unallocated space, like the one circled in red. This space needs to be formatted into an NTFS partition. Basically you can just right-click it, choose to create a new simple volume and click your way through the setup, you'll create one big partition by doing that. Afterwards the new drive should show up on Computer.
Nearly the same goes for drives or partitions with Linux operating systems or similar which Windows cannot read. These will be displayed in the device and disk management but not on Computer, so if you don't need the old operating system any longer and want to use the drive on Windows, you'll need to format it to NTFS first.
Missing drive letter
Another common source of confusion is a missing drive letter or path on a drive. The drive letter is the letter in front of your drive or partition, for example C:\ on your main drive. Every drive needs one so you can access it and if it's missing for some reason, the drive will not be shown.
The solution to that problem is in Disk Management again, so head there as described above and right-click the drive that's not displayed (you'll most likely notice it by the size). If the drive is already formatted, right-click it and select Change Drive Letter and Paths.... Add a drive letter of your choice that's not already taken and the drive should show up again.
Disabled or offline drives
It can happen that a drive of yours is disabled or offline. You can check in the Device Manager if that is the case. Go there as described above and right-click the drive you want to check. If you have the option to enable it or put it online then try that. If these options fail it might be that the drive is corrupt.
Show empty drives
Windows hides empty drives by default. This usually should not be an issue if your drive is formatted but you can change the setting anyway if you want to. Go to Control Panel > Appearance and Personalization > Folder Options. In the View tab, uncheck the Hide empty drives in the Computer folder box.