Generally, commercial/private rv parks have a sewer connection at your site. Hook up to that with your sewer hose and let gray water flow, hold black tank until it is say, 3/4 full..then dump black, flush hose with gray water and repeat as long as necessary. Those that don't have sewer at your site, will usually have a dump station somewhere on premises. Which means you either have to move rig to the dump station or use what some refer to as a 'blue boy'... portable waste tank--usually on wheels that you lug by hand or pull with your vehicle. We carry an 18 gallon blue boy...small enough to store and not so dang heavy if you have to drag it. Dump into that until full, empty and repeat.
Some campsites/campgrounds (particularly Federal/State) have none of the above and you have to manage water usage and when you have to dump, go find a dump station. There are smart phone apps for that and/or on-line lists of pay or free dump stations.
If we 'boondock', (which we used to do a lot of, but not so much anymore) we could get 5-6 days easy out of gray tank before dump and a couple weeks for black with no problem. Our (2) gray tanks held about 40 gal each and black I believe is around 50.
We rarely use public toilets/showers. Our fresh water tank is 60 gallons, so we run out of water before our grays are full.
Your mileage may vary