The way buttons in a remote typically work is that one side of the button is connected directly to ground and the other side of the button is connected to some control circuit and a resistor is used to pull the voltage on that side of the pin up to some positive value, usually the battery voltage. When the control circuit sees a positive voltage it knows the button isn't pressed and when it sees 0V it knows the button is pressed.
To simulate the pressing of a button you can connect an Arduino pin to the side of the button that goes to the control circuit. If you put 0V at that point by writing the pin LOW then the control circuit sees 0V and thinks the button is pressed. If you write some positive voltage (usually the same as the battery voltage for the device) to that same point then it will see a positive voltage and think the button is not pressed.
So you write an OUTPUT pin LOW to press the button and HIGH to release the button on the remote. The only caveat is making sure that you are writing the right HIGH voltage. If the remote runs at 3V then you'd need a transistor there to switch the 3V signal using the 5V signal.
If you're going to continue to refuse to give us any details to work with, then that's the best anyone can give you. Either take that or come back with some details on the circuit you want to control. Not what you think you have to do to control it, but real details on the actual circuit you want to control.