Campsites in Chile and especially in Argentina are often very noisy affairs. Especially at weekends when people go there to party. Some campsites are decent value but others are surprisingly expensive.
I expect you'll be heading down the Caraterra Austral in Chile. Several campsites along there including one on the north side of Coihaique that seems to attract travellers, and a really nice spotfurther south at Rio Tranquillo (this MIGHT be the waypoint - S46 37.975 W72 39.934)
If you're just transiting (in Argentina) you can usually camp in the YPF petrol stations. They often have BBQ stands, always have toilets (and therefore water) and a lot of them have expresso machines
. I always ask before pitching my tent but you'll often be joined by couples/families who will inflate an airbed next to their car.
Across some of the passes you'll find 'Refugios' at the roadside. They're triangular shaped, made of concrete blocks/tin roof and designed for emergency use (in winter) but I've slept in a few of them.
If you're going to camp in the Andes be sure to have a decent sleeping bag. I had two nights at -10 C in Chile and Bolivia, by comparisson the Salar de Uyuni was 'only' -6 C.
In Punta Arenas you can pitch your tent in the garden of Hostel Indepencia (head up the hill on Indepencia and its on the right). It was like a refugee camp when I was there. Excellent, friendly owner.
Bush camping is definately something you get better at with time. You just seem to develop a knack for knowing what and whee to look. That doesn't mean of course that you never stitch yourself up - I still manage that regularly.
Anyway, my personal No1 rule is to not let anyone see where you go. If I'm driving along a road and spot a track with potential I won't turn onto it if I'm in view of other drivers. I'll keep riding until they're out of sight then return to the track.
If that's a fairly well used track then I'll try to turn off it again and so on until I think I'm going to remain undisturbed.
Getting off the tarmac and onto the dirt roads will increase your choices immensely.
I avoid camping near towns and villages.
I don't have a campfire unless I'm really out in the boonies or with a few other riders.
If I've stitched myself up by riding too late, or just happen to be in an area where I'm struggling to find somewhere I'll wait until after dark to pitch my tent and break it down before sunrise.
As for Bolivia - don't forget to camp on the Salar de Uyuni. See 'July' in the 2011 Horizons Unlimited Calendar.
Hope that helps
Enjoy your camping, its a beautiful part of the world to be outdoors.