Nick,
Backspacing is the distance from the inside rim to the mounting surface. If you laid a wheel down on its face (the outside) and put a straightedge across the top (the inside of the wheel when its mounted), the measurement from the bottom of the straightedge to the hub surface (the part of the wheel that sits against the brake drum or hub) will be the backspacing.
Offset is easier. It's the distance from the centerline of the tire to the mounting surface.
I know very little about this subject, but I do know that the earlier (about 1994-1999) second generation trucks came with wheels that had a bit less backspacing (and offset too, I think) than the later second generation trucks.
Some Rickson wheels are made for one or the other set of trucks. As it turns out, I got some wheels secondhand that were made for the earlier trucks. I installed them on my later truck. According to most sources, this should have caused them to stick out several inches more than the original equipment tires. They didn't.
Because the wheels are somewhat narrower, the tires actually stuck out only about an inch more than the factory Michelins. Those were mounted on the factory aluminum rims.
Keep in mind that if you have mud on the lower portion of your doors, this will get worse the more your tires stick out. The Dodge accessory mud flaps help.
I can't answer your question about actual numbers, but you can remove one of your wheels and measure the backspacing. Measuring offset will be a bit more difficult, but possible, especially if your wheel/tire assembly rests on the tire sidewall when its lying down.
Regarding the tire sizes you mentioned, the 315's will be about 30 mm wider than the 285's you have now. That's about 1-1/8" wider. Half that is about 1/2", which should be about how much farther out the 315's would protrude.
I'm sure there will be others who can help out here soon.
Loren