This should be very easy, even for someone with little or no experience.
The hard drive on your laptop is located in the left top corner - as looking
at it in normal viewing/user mode - in the area underneath the ESC key.
It's basically inserted into the side of the case, much like the CD/DVD ROM.
Turn the laptop over and remove the small screw from the bottom of the case
that is securing the hard drive. Then pull the hard drive out. You might
have to exert a little force, but don't worry. You won't hurt anything.
Dell uses a specially-designed "caddy" that houses the hard drive and holds
it in place. Also, in the ones I've seen, there is a IDE pin adapter that
must connect to the hard drive pins before the hard drive will fit the
internal connector. Don't let that scare you. Just remove the hard drive
(you're actually removing the caddy) and look closely at things. You will
see what I'm talking about.
You can consult the online C610 service manual here:
http://support.dell.com/support/edocs/systems/latc610/en/index.htm
good luck,
jm