This is an external enclosure. It would depend on if your hard drive is 3.5" or 2.5". Also if the drive is SATA or IDE. From your post it is most likely IDE.
You need to make sure which you have. A SATA drive will have a red or grey cable from the motherboard to the drive. An IDE drive will have a grey flat cable. The drive on the left is IDE.
If this is a desktop you probably have a 3.5 drive vs 2.5. A laptop would be 2.5
The size and format, IDE or SATA depends on what USB enclosure you get.
Here is an example of a 3.5 IDE enclosure and here is an example of a SATA enclosure for a 2.5 drive. Here is a USB adapter that can be used for IDE,SATA, 3.5, and 2.5 drives. I would recommend you have somebody with computer experience help you do this.