Before attempting to change a cooling unit, read the cooling unit safety page.
Many things could be considered a factor in the proper installation of a cooling unit, but what we are concerned with here is the actual fit between the cooling unit and the rest of the refrigerator. A proper fitting cooling unit is crucial for good operation, and is not an area to compromise.
Cooling is the removal of heat from one point and transferring it to another. In an RV refrigerator, heat is transferred from the refrigerator box to the cooling unit via the freezer plate and fins. Usually the fins and freezer plate are fastened to the cooling unit so that they can be removed if the cooling unit needs to be replaced. Thermal mastic, a heat transfer compound, is applied between the cooling unit coils and the contact points of the freezer plate and fins. It is very critical that these contact points have no gaps between them, their fasteners are snug, and that thermal mastic is applied between them. Failure to do so will cause cooling problems.
In the graphics below, the 
is a metal to metal contact point that requires thermal mastic. The 
refers to a fit point -- a point where the cooling unit has to make good, snug contact with the refrigerator box. The Type 1 cooling unit below covers the basics for all cooling units and should be read no matter what type you have. The Type 2 and 3 instructions only cover additional information for the specific types.
Type 1. (Above) The foam block of a cooling unit is not a precision part and often doesn't fit right when one cooling unit is being exchanged for another. It may need to be trimmed or it may have gaps along the sides that need to be filled in. It's a good idea when installing a cooling unit to first place it into the refrigerator to see how it fits before committing to the installation. This is also a good time to see if screw holes on the cooling unit line up with holes inside the box and to compensate if they don't. The cooling unit needs to fit all the way into the refrigerator cavity and not be held back by any part of the foam block. The sides of the foam block need to be sealed with permagum or silicone to prevent air leaks. Other parts of the cooling unit give off heat and the slightest air gap around the foam block will allow this heat into the refrigerator box and diminish the cooling. The foam block always has a backing of some sort. This backing should be secured to the refrigerator with screws or tape. Whatever can be done to prevent air leaks into the box around the foam block should be done (putty tape, duct tape, silicone, etc.).
All the diagrams on this page show removable fins (when applicable) being installed to the cooling unit before the cooling unit is installed into the refrigerator box. This is true on all larger boxes (6 cu ft and larger) except the Dometic RM100, but is not true for many smaller boxes. Sometimes the fins are designed to be installed from inside the refrigerator box after the cooling unit is installed. The key word here is "designed". The fins need to be installed in the same manner as they were originally installed from the factory.
Type 2. The installation shown below has the same requirements as the installation above, as do all cooling unit installations. The difference in the cooling unit below is that the freezer coil protrudes horizontally into the freezer instead of being embedded vertically into the foam block as the model above.
The freezer coil needs to be perpendicular to the cooling unit body. If this coil is visibly bent upward or downward (usually from shipping or handling), it needs to be corrected.
A crow bar placed around the center coil (not shown) can then be leveraged against the front of the coil to bend it. If you plan to change many cooling units, a homemade bar with a tighter curl would be worth making and easier to work with.
Older Models Many older refrigerators had the freezer coils of the cooling unit fastened to the freezer floor. (Below) Many of these older cooling units also had fins built into the cooling unit and were not removable.
Screws through the freezer floor, on the style above, pull against brackets attached to the freezer coil to insure contact between the coil and the freezer plate. This contact is crucial. Be sure all screws are tightened enough to pull the freezer coil to the freezer plate. Sometimes finding the holes in the freezer brackets is difficult. Poking around with an awl or ice pick can be helpful. Also, when installing one of these units, it's a good idea to get to the freezer plate screws early, since if you can't find the brackets with the freezer screws, you may have to pull the cooling unit to correct the problem.
Mounting The cooling unit is mounted to the refrigerator box with screws or bolts. The location of these screw holes on the refrigerator back and cooling unit insure that when the cooling unit is installed, certain critical angles of the cooling unit coil are maintained. Sometimes a cooling unit is bent in shipping, but can be "stretched" to make the holes line up. Other times the cooling unit may be too severely damaged and may have to be replaced with another one.
It would be simpler to say that all screw holes on the cooling unit must align with the holes in the box, but this isn't absolutely true. The more important mounting holes are on the top half of the cooling unit. It's very important that the condenser at the top of the cooling unit be at a certain angle. The graphic above is generic, meaning that the angle of the condenser shown is not correct for all models of refrigerators. On some models the condenser is almost level, while on others, there is a distinct up hill slant. The point is to be sure to maintain the original angle when changing a cooling unit.
Another important angle is the angle of the boiler and rectifier (often one pipe). The boiler is inside the insulation pack. The boiler and rectifier need to be parallel to the side of the refrigerator, or perpendicular to the bottom of the refrigerator. If existing mounting holes on the refrigerator allow this to happen, great. If not, it is acceptable, to push the bottom of the cooling unit one way or another and start new holes.