This page was taken from Ken Chan's Neon page with premission from the owner.
I have taken apart every piece of the dash at least once so I speak from some experience.
The first thing can be taken apart is the center bezel where the controls for the Heat and Air are located. To do this you must first remove the ash tray. To do this open the ash tray and then pull the ashtray down and forward. It should pop out of a couple of metal springy clips. Next, to remove the center bezel, just pull along the edge of the bezel along the sides and the bottom. Just carefully work it loose. A few metal/plastic clips hold the piece in place, and should pop out when some pressure is applied. There are no screws here so don't worry about wrecking stuff. It's almost like playing with LEGO (tm) sometimes you gotta pull really hard and then it just pops open, but nothing broke in the process. Just as easy to replace. This gives easy access to the evironmental controls as well as the radio.
The next part of the dash that I took apart was the top cover of the dash. I did this by simply pulling along the edge of the cover near the instrument cluster. Just do this firmly but gently and it should also pop apart like the center bezel. Note that there are a couple of clips on the passenger side of the cover also. Once the top cover is removed the instrument cluster is revealed and so are a bunch of wires and the passenger side air bags.
You can then remove the instrument cluster if you have a bendable rachet type screw driver or if you have short screw drivers and very dexterous hands. If not you may have to remove the left trim (heat vent) panel. This involoves removing the steering column cover and steering column cover liner because the left trim is screwed together with the steering column cover liner. Once these are removed you shouldn't have any problems with the instrument cluster.
The instrument cluster is held in place by four screws along the corners of the cluster. Once the screws and the instrument cluster are removed then you will see two connectors. The left one is J2 and the right one is J1 (closest to passenger in US cars). The J1 connector contains the Tach wire.
The last thing that may be of interest is the removal of the fog light and defrost switch. This plastic panel may be removed by using a flat screw driver and carefully wedging the panel out. It is also clipped in by plastic clips.
Also note that the center console may be removed. To do this just unscrew 1 screw in each cup holder and a couple of screws behind the E-brake in that little bin. The screws may be hidden by a little plastic cover. Then just pull the center console at the E-brake location upwards and the plastic console should slide right off.