When I plug in an external hard drive the computer recognizes it on the bottom task bar with the icon safe to re move mass storage but I can not find it on my computer to up and down load

Does it work if connected to a different computer. If not then perhaps the drive is defective.

If it works, then does it show in Disk Management on this computer? If so, can you assign a drive letter to it?

Click Start then Run, type diskmgmt.msc and press Enter