Do I rinse it out with just plain water?
Yep - 99% of the time lots of flushing with plain (cold or cool!) water is all that is needed. I’ve heard of adding a bit of of ammonia to the water for really stubborn clean-up, but so far (fingers crossed...) I’ve never had to resort to that.
I usually put some water in a cup and just keep changing the water until as it gets colored, until it runs clear.