What airspace are ultralight pilots allowed to use? So I've been watching videos and thinking about getting into ultra-light aviation. Flying in a personal air-trike or paramotor looks like a lot of fun. Being new to the aviation arena I had a couple questions:


How do the airspace restrictions work? 
Do you have to file a flight plan like any typical aircraft/pilot at an airport? 


For example, say I wanted to take my paramotor to a large park and take off from there? How would that work with the FAA, talking to ATC and other traffic in the area so they know I'm there? Does it work the same as flying in a Cessna?
Ultralights are regulated under 14 CFR 103. There are very few regulations that apply to them, but there are specific rules on airspace in 103.17:


  §103.17   Operations in certain airspace.  
  
  No person may operate an ultralight vehicle within Class A, Class B,
  Class C, or Class D airspace or within the lateral boundaries of the
  surface area of Class E airspace designated for an airport unless that
  person has prior authorization from the ATC facility having
  jurisdiction over that airspace.


That means, you can fly in (most) class E airspace and all class G airspace. You can find more information about those airspace classes in this question.

As for your other questions:


A flight plan isn't required even for aircraft, and ultralights aren't subject to the regulations that would require them anyway
Ultralights aren't required to have radios or talk to anyone; you usually fly so low that you aren't in anyone's way
It's not at all the same as flying a Cessna; in fact, you don't even need a pilot's license to fly an ultralight
See this question for information about launching from national parks; state parks would be subject to state law instead but the principles are probably the same


You might want to look through all our ultralight questions for more information.