It _is_ an external hard drive, now.
Okay, seriously. You can buy an enclosure for the drive that will make it into an external hard drive - USB, eSata, FireWire, take your choice. The other choice is to buy an external hard drive, connect the removed drive to an existing computer, and copy.
How you do either of these depends on two things: The size of the hard drive (3.5", 2.5", 1.8") and the connection type (IDE or SATA). If you don't know how to recognize these, the make and model will be on the big sticker on the top of the drive and we can look it up.
To put it in an enclosure, you buy something like this: http://www.newegg.com/Product/Product.aspx?Item=N82E16817388035
Otherwise, buy an external drive and, temporarily, connect your existing drive to a PC. Got a spare PC around? If it's a tower, and you are comfortable opening it, you could connect the old drive to a port on the motherboard. Otherwise, you could buy a temporary adapter like this: http://www.newegg.com/Product/Product.aspx?Item=N82E16812156017
So: What kind of drive is it, and which method do you want to use?