In order to access/read an external hard drive on your Mac, all you should need to do is plug it in and open it from the Finder sidebar. However if it is not showing up, then most likely the external drive is using a format MacOS does not support.
Open the Disk Utility on your Mac, and see if the drive is showing there. If not, there may be a fault with the drive itself — check it on another computer and if the result is the same, the drive is faulty. Most likely however the drive will show up in the Disk Utility, meaning it is simply using a format unsupported on MacOS.
If this is the case you will need to re-format the drive. This will clear all of the data on the drive, so if there is data on there you need you’ll have to connect it to a computer which it already works with and back it up.
Once you are ready for format the drive, you will need to select the drive in Disk Utility and select the “Erase” option. There are a few formats to choose from — which one you’ll want to use depends on what the external drive will be used with:
Mac OS Extended (Journaled)
If you will be using the external drive only with Macs, not Windows computers, then Mac OS Extended (Journaled) will work great. It is also the only option that will work with Time Machine and Time Capsule, so if you want to use the drive for Time Machine backups or attach it to a Time Capsule to access files over the network, you must use this format. Be sure to use the Journaled option, not the Case Sensitive one.
If you want your external drive to have the most universal compatibility possible, then select this option which will format the drive (most likely) as FAT32. The FAT32 format can be read by Mac and Windows computers both old and new, in addition to other devices such as TVs. However its major drawback is the file size limit of 4GB. You cannot copy a file to a FAT32 drive if it’s over 4GB, which can be very restrictive. If this doesn’t matter to you though then you should have no problems with FAT32.
The ExFAT format supports both MacOS and Windows, but unlike FAT32 has no file size restriction. This makes it ideal for external drives, providing you don’t need compatibility with old devices, 10-15+ years old. Out of the three main formats, ExFAT would be the best all-round option for external drives.