Assuming that the hard drive is not the part of the system that died, then yes it will be easy to get the data off. You can either, as you said, plug it into an external HDD caddy, however the easier way would probably be to plug it in in another computer internally and copy the data using that computer.
The easiest but more expensive (in that there is a cost) way is to get a hard drive docking station such as this one (Newegg.com - Rosewill RX-DU101 Plastic 2.5" & 3.5" Black USB 2.0 Docking Station
) which plugs in via USB. But I'd recommend the connecting-it-internally route since assuming you have cables that will be free (and inexpensive if not).