Every national park has an awesome web site. Check them out before making plans. They give things to do, camping, road information, special alerts (fires, flood, road wash out), etc.
Below is the one for Arcadia NP. You want to use the 'nps' sites for the official web site.
Under 'Things to Do' there is a eating/sleeping section to click on. Then it will show 'campgrounds' and all the information will come up, including a 'clicky' for getting reservations.
Every campground in national parks don't require reservations. There are usually first come campgrounds, including in busy Yellowstone. For those, you would need to stay outside the national park but nearby the previous night and then drive into the park and non-reservable campground early morning when folks are leaving. Even with our 40' motorhome we always got a site without reservations but then we were retired and had the time to deal with getting there early. For those on a specific vacation time it's best to stay where you can make reservations.
To answer your question, no, you can't just park anywhere and camp. It needs to be in a designated campground.
You might be thinking of boondocking on public lands such as national forests. Then you can be more flexible with parking as there aren't designated campgrounds. It's called 'dispersed camping'. However, they still ask that you use a pre-used spot and not drive through the vegetation creating your new spot. We have also done this kind of camping a lot and it's very enjoyable. You might want to stop at a national forest ranger station to ask where you can do this until you get the hang of it. State forests are run differently so you'll need to ask there, also.
There are many, many lovely national forest campgrounds where they have designated sites. Usually those would be on or near a lake or stream so that might be of interest to you. Some are dry camping - no hookups - but some have electric and some have dump stations. Each one is different.
Here's a national forest site that we used a lot. You first need to know what the forest name is where you want to stay. Some maps show the names. Then click on the forest and a list of campgrounds comes up with lots of good information including directions.
https://www.forestcamping.com/dow/pictures/pictures.htm
https://www.nps.gov/acad/index.htm
We enjoy all of this type of camping rather than a close-knit RV park where all you see are other RVs. We like nature! Good luck to you.