In a nutshell all State Parks require you to pay/reserve a site to camp. You must stay at a designated site whether it be the type that you drive up and park at your site or whether you park in a State Park parking lot/trailhead and hike in to a backcountry site. When you ask a Park Ranger about hammock camping just leave the word camping out of the question. They already know you intend to camp. Just ask if you can hang a hammock at your site. Most State Parks allow it but some don't.
For Federal wilderness areas there is no need to ask about hanging a hammock. Just do it and remember the Leave No Trace principals. If there is a bunch of green on the map than there are trees to hang from. Parking: There is a thing called a trailhead. That is where most folks will leave their vehicle or get dropped off and backpack in. If you pick up a detailed topo map you will see known/named trails and most will show trailheads. Some trailheads are tough to get to while others are easy. Not all trails have trailheads. Some trails are only accessible by taking another trail to get to it and so on and so forth. This information could go on and on.
Lastly, I don't want to make you feel bad or discourage you because I do encourage you to get out there and experience the great outdoors. Until you get more experience I suggest that you stick with places that don't require navigation, map or compass skills. You might want to go with someone with experience or stick to trails that are well traveled and well marked. There are actually quite a few of them.
Good luck to you and remember to have fun.