The drive is screwed to a plastic sled which slides and clips onto the internals of your 610's case. I forget which, but there is a release tab on the sled either at the the front or rear underneath the drive (there were several basic designs and I get confused about what fits in what). Once you find it, push the tab down in order to slide the sled out; if you use brute force, it will usually also come without any attention given to tabs, but that's not such a good idea.... You may need to remove the thin metal RF shielding at the front of the case, if present, in order to get the old drive out (and the new one in). You will also need a medium or smaller Philips screwdriver, unless someone has used non-OEM screws.
Remove the screws holding the old drive to the plastic sled. Pay attention to any jumpers placed on pins on the base of the old drive and deplicate the arrangement if possible on the new drive. In particular, if jumpers labelled TE or Term are present, they must be jumpered. If they are not present, worry not -- termination can be automatic. You may need to find a manual online if the drive is one of the more obscure ones, or one without Apple Roms that has been adapted to run on a Mac. The SCSI ID number can be ignored as long as it is not set to 3 (the likely ID of your CD drive), and in fact, no jumper for the ID is the recommended arrangement for a boot drive (then the ID = 0).
Connect the scsi ribbon, power connector, and test by booting or attempting to boot. If it works as expected, shut down, disconnect the new drive, screw the new drive to the old sled, using the screws removed that held the old one. Install your new drive permanently and your software as required. Enjoy.
Our collective fingers are all crossed.
This is not going to involve a huge effort, and there is not really much to go wrong on the mechanical side of things. Relax and enjoy this first encounter as a hardware tinkerer.