Turned arduino 5vdc analog pin to 0vdc (gnd) in order to mimic a momentary switch
What interface you will need depends on the circuit of the remote. If the switch shares a common ground with the Arduino then you might get away with just connecting directly to it. However for safety I would use a diode or transistor to provide an 'open collector' output. The circuit below shows how both a diode and transistor would be wired (choose one or the other, not both!). 



Some remotes have their switches connected to battery positive, perhaps to make the transmitter turn on whenever a button is pressed. Others have buttons arranged in a matrix of rows and columns, so both ends of the switch may be floating. In these cases you can use an opto-coupler or PhotoMOS 'relay' (opto-coupler with FET output). 

The circuit below shows how to use an opto-coupler. Note that the opto-coupler's output is polarity conscious, so you may have to swap pins 4 and 5 to get it working.