If the tanks are full, they need to be dumped at an appropriate dump station first. Some state parks allow dumping even if you are not camping, they charge a fee, but they are one place to dump at. Other campgrounds may offer that as well. Call ahead and ask. And yes, I have seen first hand a camper sold used and they left the black tank with a good amount of black tank matter it. YUK....
To check the black tank, push the foot pedal on the toilet to open the slide gate or ball valve pending the brand, and with a flash light look down the hole. You should see the bottom of the tank as a good clue the tank is close to empty or is empty. It may have a wet sheen on the bottom of the tank or be totally dry pending when the last it was used to be considered empty. If you see liquid, you can check the depth with a stick and the determine what to do.
To clean the black tank, you get a hose wand sprayer that fits on the end of the garden hose. There are different brands of these, this is a good one. https://www.amazon.com/Valterra-A01-...YDO/ref=sr_1_2
Then put the spray wand down the hole inside the camper and blast in all directions inside the tank. Ideally the dump valve is open and can drain out whatever is in the tank during the water blasting process. This does a good job cleaning out the tank pending how long and how dried up the prior owner kept his tanks.
The grey water tank cleaning is different as you cannot get a wand in there. And soap skum and other matter can grow on the top of the tank over time. I have used Happy Camper Extreme cleaner to clean out the grey tanks. This product https://www.amazon.com/EXTREME-CLEAN...VVC/ref=sr_1_4
With the grey water tank dump valve closed, you fill the tank part way, then mix up the Extreme cleaner in a bucket of water and pour it down the shower drain, then keep filling the grey tank with water from a faucet or a hose down a drain until the water backs up in the shower basin drain. The shower drain is most times the lowest drain point inside the camper and when it starts backing up, the tank is totally full and the pipes up to that point. They let the mix sit overnight, and drain and flush with clean water. This can also work for the black tank if there is a lot of dried up build up.
The key to keeping clean tanks, is once they are clean, keep them clean. Flush out the black tank after every campout or every dump, use a lot if water. You also need starter water in the bottom of the tank at the start of as campout. Put enough water in the tank so you can see about 1/8" to 1/4" of water in the tank under the toilet dump area. This starter water stops solid sticking in a pile under the toilet dump area. The matter will float in stead of pile up.
Then once clean, create a tank treatment program. This topic ranges all over on personal opinion from do nothing to strong bleach or preserving chemicals. I ,self use Happy Camper tank treatment in the black and grey tanks both each campout and I have installed internal tank sprayers in both tanks so I can flush each tank every time I dump. This product, it is different then the extreme cleaner https://www.amazon.com/Happy-Campers...ADU/ref=sr_1_2
I also have access to my septic tank at home for cleaning up the tanks some times when I have to dump and run at the camp ground as there is a long line behind me. I do not want to hold up the line with the tank sprayers then. And I do not want any bleach or other preserving waste chemicals to go into my septic system at home. The Happy Camper is an sort of advanced bacteria and enzymes type of product to break down the waste and breaks down the bacteria that makes the smells.
Hope this helps and good luck with your new camper!