By external drive you mean a hard drive which was taken out of a laptop, right?
In that case you need an USB "external enclosure". You can put your hard drive into it, then you can connect this to your computer via a USB cable, it shows up as a new drive and you can browse the filesystem and copy files over.
Note, that these enclosures come in different flavours depending on hard drive size (2.5'' for notebook drives, 3.5'' for PC drives), and hard drive connector type (SATA for newer, IDE for older generation hard drives).