Is the drive recognized by Disk Management? If so, you can go to Disk Management and see whether the drive has a letter assigned. If not, you can assign one. Check this out: http://products.wdc.com/support/kb.ashx?id=aVRM5F
If the issue persists, and after the external drive gets recognized on other computer but not on yours, I would suggest you to update your USB drivers. You can find them on your laptop manufacturer's website.
You can try the drive to all the ports on your laptop. It may be a good idea to use a different USB 3.0 cable as well(Y type of one preferably). It will not hurt to test the drive with a brand specific tool as well.