A flight plan can take many forms. There are filed flight plans, often referred to as FPLs, which include a whole load of info about the aircraft, its capabilities, intended route and so on. These get submitted in a very specific format used all over the world - you can see one along with guidance about how the information is entered
here. The way that some of the aircraft capabilities are entered and some of the rules for item 18 changed a couple of years ago but the form itself hasn't changed.
And then there abbreviated flight plans, there are different names for some different purposes but for something like circuits for training or short, A-to-A test flights it may be as simple as a phone call to the ATC tower to say "We'd like to do 5 circuits, one rejected take-off, three people on board, call sign will be....".