Your City Water Hookup will not fill the fresh water tank. That hook up is used when you are at a campground with a water hookup. Always use a RV water hose specifically for POTABLE (clean,drinkable) water - not a standard garden hose. To use that hookup, connect the water hose from your water spigot to the city water connection. You may need a pressure regulator if you have really high water pressure, depending on the age of the RV. You can pick that up for just a few $$ at walmart. It goes on the end of the hose between the spigot and the hose and will keep the water from being too high pressure that can damage the RV.
Anyway, once you have the hookup connected, turn on the water full bore. Then turn on the spigots in the camper. You will have to have them open so the air in the lines has somewhere to go. It may take a minute or two, but you should get water flowing out of your sink faucet once the hot water tank fills. With the city hookup you leave the water line connected and turned on - there is no tank being used and so it relies on the water pressure in the line to run the water through. It also bypasses the water pump since again, the water is already pressurized from the city water line.
The other opening for fresh water is the 'potable' water tank. That one is more of a cap type that will open and you can hold the hose pipe up to the tank to fill it. That one you will need to sanitize before you go camping the first time, but to test it out, make sure the drain valve is closed (it will be somewhere under the camper) and then just run water into the inlet. It will not over fill, as once the tank fills up the water will run out the overflow. Once the tank has a few gallons at least, THEN you can turn on your water pump and you should get water coming out of the TT faucets. Same thing applies as running off city water hookup - you'll have to run the water a little while to get the air out of the lines.
Once you've tested the system, then you want to drain the fresh water out and sanitize before you actually try to drink or cook using water from the water tank.
-you don't have to fill up the water tank at all if you are camping at places where you will have city water hookups. We never keep our tank full - for our TT it's over 300 lbs of extra weight sloshing around while on the road, and we always camp where we have water hookup at least.
-We do usually travel with a little (5-10 gals) of water in the fresh tank in case we want to stop and use the potty or wash hands from the TT while enroute
-before you actually use the water from the fresh tank, you do want to sanitize your system. Here's a great video about sanitizing How-To Sanitize the RV Water System by RV Education 101® - YouTube
if your owner's manually isn't very detailed. Actually, anything by that same guy (RV Education 101) is pretty good.
Ditto what was said about the black tank - if your sensors are reading that there is something in the tank but there isn't then it's probably gunk stuck to the side walls. Your camper may have a black tank flush system built in, but if not, there are videos on that too...HOW TO: Hook Up an RV - YouTube
RV GEEKS have some great videos too.
Hope this helps! Keep the questions coming and enjoy your new RV - we all were newbies at one point too!