Basically what happens is that you are altering the way in which the circuit works. For instance, by adding another capacitor in parallel with a timing capacitor, you slow down the timing, which might make an oscillator run slower or slow down an envelope. By shorting two pins on a chip you might put it into an odd mode, not used in that piece of equipment, or you might crash the CPU in a computer-controlled device causing it to send garbage to the sound chip. With a ROM-based sample-player instruments (like the Alesis HR16) then if you earth one of the address lines, you will only play back half the sample. Which one depends on which pin you earth - if you earth A0 then you will only ever play back even-numbered samples (half the bit-rate). If you earth A3 then it will repeat groups of eight samples twice, and so on. The really interesting thing about bending sample-based stuff is that it is entirely predictable - you can always tell what it's going to do, and have some idea of the effect you'll get.
Now, with the Speak'n'Spell you've got a simple microprocessor which slings a string of bits to a sound chip. You'd be surprised at how simple it is. Read some data (not samples, we'll come to that), push it out a serial port, and then the sound chip will turn it into Dalek-y speech. Simple. When you crash the CPU it runs off into the weeds and starts slinging odd fragments of words mixed with bits of the program code out to the sound chip, with hilarious consequences.
To pack recognisable speech into the low-capacity ROMs available in the 70s and 80s, Texas Instruments used a codec called LPC-10. Now, this is not so much like a sample as an MP3 in that the data doesn't directly represent the output waveform, it describes how to generate it. The data encodes pitch, timbre and volume information into packets that are turned into sound by what is more-or-less a complex hybrid digital/analogue synthesizer. Now, one of the the interesting things is that you can get software implementations of the LPC-10 codec, and run them on your PC. You can have a lot of fun compressing and uncompressing stuff, and introducing random bit errors to the data. Or, you can be totally bizarre and use LPC-10 to play back utterly unrelated data, like this:
http://www.gjcp.net/~gordonjcp/lpc10.mp3I'm planning on (finally) launching my new website in a couple of days, once I get a few more articles written. There's quite a lot of technical information on how sounds are generated, which might help you. I'll post a link later.