There are many things that a person might need to do to their car which are very simple tasks with the instrument cluster removed and are virtually impossible with the instrument cluster still in the car, such as replace the headlight switch or replace one or more of the light bulbs back there. Removing the entire cluster can seem like a scary proposition if you are unfamiliar with how all of that junk back there goes together, but it is not a big deal at all.
First, disconnect the negative battery cable from the battery. Next, you have to disconnect the speedo cable. There is only one route that your hand can take to reach it. With the driver's side door open and you on your knees outside of the car, you have to run your hand up between the emergency brake handle and the air vent cable. From there, you keep running your hand up until you locate the speedo cable. Where the speedo cable goes into the back of the instrument cluster there will be either a round, gnurled knob thingy or what feels like a big hex nut. Either way, you just unscrew that and pull the cable out of the back of the speedometer. It might be a little snug, but fortunately, there was no way for the last owner to get a wrench on that, or tack weld it in place, so you will be able to unscrew it by hand. I don't have any trouble at all getting my hand up there, but men sometimes find that their forearm is just a tad too big to squeeze in there. If this is the case, just take those two big screws out that are holding the emergency brake handle assembly and the air vent knob to the dash and that will give you enough room.
Once you have the speedo cable loose, remove the six screws that hold the instrument cluster to the dash. There are four along the top and two on the bottom. Work the instrument cluster out far enough to start unhooking all of that stuff back there. The wires just unplug and the bulb sockets just pull out. Once you have every thing unhooked, remove the instrument cluster from the car. Be sure and have a towel or something on the steering column because you will definitely scrape up the paint if you don't. The second picture is color-keyed to show you how the wires and bulbs go back on. There will also be an instrument cluster voltage regulator with three wires attached to it. Two of them will be dark green with a black stripe, and one will be black. How this works is in the section on gauges, along with the wiring diagram, but, the black one is the dash ground and the two green with black stripe are power-in / power-out for the instrument cluster voltage regulator. The third picture is to show you exactly where the speedo cable is attached to the instrument cluster.
This has all been for either a 66 model car, or a 65 that that has gauges instead of idiot lights. A 65 with idiot lights is just like a 66, except for you just unplug the lights instead of some wires. On some, you have to twist the idiot light sockets and then pull, and on some you have to just pull the bulbs out. On a 65 with gauges, there will be a big wire going through a loop on the back of the ammeter gauge. The wire has a disconnect that you can unplug several inches back from the gauge. When you run the wire back through the loop to re-install the instrument cluster, be sure that it goes through the same way it came out or your ammeter gauge will read backwards.
When you re-install the instrument cluster, it is very good idea to hook everything back up except the speedo cable and, before you put the six screws back in, re-connect the battery and check to see if everything works like it's supposed to, so that, when you hit the left turn signal, your high beam indicator isn't the one that starts blinking. It is also a very good idea to, while you have the instrument cluster out, replace all of the bulbs. They are available at any auto parts store and are cheap. The part number for the bulbs is 1895. Nothing to it.