Hi @Alice McCoy
Remove the batteries from the remote if you haven't already done so and then you will have to open the remote and use Isopropyl Alcohol 99%+ (available from electronics parts stores) to gently clean away any remaining coffee and also any corrosion that has started to occur on the board.
Check for any screws in the battery compartment that may be holding the remote case together and if none there you will have to pry open the case along the seam. usually there are plastic locking tabs that have to be prised apart.
FYI rice doesn't do anything to fix the problems caused by liquid damage. Here's a link that may be of interest [https://www.ifixit.com/News/30047/rice-is-for-dinner-not-repair|Rice is for dinner, not repair]