You need to take the hdd out of the external casing and open up your computer and connect the sata data and power cable to the hard drive and it will show up in my computer. If you don't have any spare data power cables coming from your power supply then you will need to buy a 4x peripheral molex connector to sata adaptor. If you don't have a spare sata data cable you will need to buy one of those as well. They are not expensive they usually cost about $3
And if it appears to be hardware problems with the disk and you really need your files back, don't rely on any software, go to a data recovery pro.
Keep in mind that if the problem is simple, it won't cost you much, if the problem is serious, you won't be able to solve it yourself, you only deteriorate the situation.
------------------------------A backup a day keeps data recovery away. Reply to alt-rtt
You can easily recover your hard drive.Sometimes hard drive get corrupted due to virus attacks, scratches on the hard drive, formatting/reformatting the hard drive or many such reasons.In such situations the file will not get open easily.Hence by using a good hard drive recovery software,you can easily recover your corrupted data and save the files on you computer back.Hard drive recovery software is a very effective tool and provides complete recovery of corrupted data.For more information you can check the link: http://www.datarecovery-software.net/external-hard-drive.html.You can easily download the free trial version of the software.