Call the ranger back, and ask him/her the rules for backcountry camping at your locality. Around here, it can mean anything from using designated sites (semi-developed with an outhouse and/or water source, to undeveloped; with or without a fee) to "anywhere you can find a flat spot." If it's the latter, there are usually local rules that require you to be a certain distance from the trail, stream, parking lot, or campground. There can be other local peculiarities, too. ("Don't camp in Primrose Valley from March to June; that's when the Endangered Raptors are mating and nesting, and we don't want them disturbed." "Don't camp by Rip Roaring Creek if rain is forecast - it floods too easily, and we don't need another 6-campers-dead incident this year.")

Another consideration is impact. The general rule would be that dispersal is better - use the un-obvious site to minimize impact. However, in the heavily used areas in the eastern US, the backcountry managers may tell you to use the impacted sites instead. You can't impact them any more than they already are, and continuing to use established sites spares areas that haven't been beaten up yet. Around here, if I don't want to use the established site, I'll usually look for a durable surface, such as rock (bare sandstone slab, for example) and rely on my Thermarest for comfort instead of forest duff.

Along those same lines, plan to use a stove rather than build a fire. Fires nearly always leave a trace: charred wood that's visible even when scattered, blackened rocks from a fire ring, etc. Beyond lowering impact, stoves are also less hassle than fires: there's no firewood to gather, no blackened hands or pots, no facefuls of smoke, and no hauling water to make sure it's dead out before you leave. (Having to haul water for a fire also pretty much ties you to camping very close to a stream, which limits your possible campsites - another bummer.)

Oh, and if you do commit a faux pax - own up to it, apologize, offer to correct the matter (even if it involves packing up at dusk and hiking another mile), and explain that it's your first real backpacking trip. Then ask for any tips they might have. Rangers sometimes have a policy that forgives first-timers who are willing to be educated, and other hikers are always glad to play "expert" for you.