Here are disassembly instructions for a few selected calculator models.
Disclaimer: if you take apart a vintage calculator, you do so at your own risk. I am not responsible for any damage that results from the use of information found on these pages. Also take note that many calculators had multiple versions; the disassembly instructions presented here may not be applicable to the calculator you hold in your hands even if the model numbers are the same.
Texas Instruments SR-52
To open the calculator, unscrew the four screws on the bottom. The calculator's two halves should easily separate, but they remain attached by the wire that connects the power supply connector. By removing a fifth screw, you can detach this connector from the calculator's bottom shell, and remove the bottom shell altogether.
To remove the card reader, you need to unscrew three screws that hold it against the top shell of the calculator. It is not necessary to remove another two (usually shiny) screws that hold the reader itself together. If you remove all five screws, the reader comes apart; be careful not to lose the nylon roller wheel that may fall out at this time.
[See also Marek Czeszek's illustrated Web page.]
To remove the back cover, first remove the battery pack, solid state software module cover, and solid state software module. Remove the two screws near the top of the calculator. Sometimes these screws are very difficult to remove! Make sure you don't destroy the screw's head by using an inadequate screwdriver; if you do, it'll be necessary to drill out the screw, which is a very unpleasant experience. In a particularly difficult case with a TI-59, I first heated up the screw (VERY carefully) a few times with a soldering iron. Watch it: too much heat and you melt the plastic, welding the screw in place for good. All I wanted to do was to loosen it a bit, so I powered down my iron and let it cool a while before use. Then I used a removable bit from a screwdriver that I secured in a vise; I placed the calculator on top, carefully inserted the screwdriver bit into the screw's head, leaned on the calculator with my body weight, and slowly began rotating it. Desperate move it was, but it worked: the screw began to move.
With the screws removed, you'll be able to slide the lower shell of the calculator a few millimeters towards the calculator's bottom, making sure that it doesn't impact against any of the calculator's electronic components inside. The two halves should unlatch, and you should be able to completely remove the lower half of the shell and store it away.
To disassemble the card reader, you need to remove four small screws that secure the card reader against the calculator's top half. When the card reader is free, you may wish to disconnect the two flexible circuit connectors that connect it to the main circuit board; however, be aware that these connectors are not very rugged, and may easily be ruined. To open the reader, it is necessary to remove the strong spring lock that secures its two halves together. Be careful not to lose the small nylon roller wheel that may fall out of the reader.
To remove the keyboard panel, you need to unlatch four plastic latches that hold this white sandwich against the top shell of the calculator. As you begin lifting out the keyboard panel, be careful not to lose any of the plastic keys that come lose at this time. (Having another calculator, or the picture of one handy is a good idea at this point.)
These Texas Instruments calculator models have a plastic shell that's not held together by any screws; instead, flexible plastic latches are used. To disassemble the calculator, it is necessary to first remove the battery pack, then open the three plastic latches inside the battery compartment. This can get tricky, as those latches have a tendency to snap back in as you're trying to unlatch all at the same time. Once successful, the two halves of the shell should begin to come apart near the top of the calculator, but they remain latched together near the bottom. Sliding the lower half of the shell towards the bottom should completely unlatch the two halves and the lower shell should separate cleanly.
To unlock the keyboard panel from the top shell, it is necessary to unlatch several small plastic latches that hold this panel in place. Be careful not to lose any of the keys at this time. If you also unlock the latches that hold the display in place, you can completely separate the calculator's electronic assembly from its casing.
An excellent article contributed by Mike Davis about repairing HP-67 card readers contains detailed, photo-illustrated instructions on assembly and disassembly.
Another excellent article, also from Mike Davis, provides detailed instructions for repairing HP-97 card readers.