I'm not sure what to call this. I have some existing hardware with buttons. When the button is pressed, something happens. I want to "catch" that button press and have the arduino read it and then do something.
My thought is to splice into the existing buttons wire, add a resistor, and wait for the arduino to see that input go to HIGH. I think the resistor will keep the voltage from dropping on the existing button. This is probably a flawed thought.
You need to supply more details, because the answer is hugely dependent on what those "buttons" are doing. Are they connecting 110V AC to a relay? Grounding a logic input to some other piece of digital electronic gear? Supplying battery power to a gadget? More than one of the above?
These are standard arcade buttons on an arcade machine. I want to press a button and have it do it's thing in the arcade game, but also have the arduino read the button press and execute some code.
You're going to have to find out how those buttons are wired inside the machine.
It could be that they're done as a simple "1 input pin per button" arrangement, like the simplest Arduino demos. That could be as easy as just wring the switches to Arduino inputs, too. It might be necessary to do some level shifting, if it's a really old and odd contraption that doesn't run off 5V.
But it's also possible that they're wired as a matrix, which would be more of a pain to leech from.