There are 4 brake calipers on most cars.
Is there a proper order in which to bleed them when bleeding brake lines, or can you bleed them in any order with the same result?
If you are replacing the brake fluid for example, bleed the corner farthest from the master cylinder first. Then the next farthest, etc, etc till you have done all four. If you're just bleeding air out of the system, that's the order as well.
Generally the master cylinder is on the firewall on the drivers side, so the passenger side rear would be first, then the driver side rear, then passenger front, then driver front.
I hope that helps!
If you're doing it right, fluid is only moving downstream so it really doesn't matter what order you use.
However, most guides will tell you to go from longest to shortest run of tubing -- this does have the benefit of the job seeming to move along faster as you go. If you wish to follow this order you should poke around and see for yourself how the system is laid out.
Many cars these days have ABS, so on those cars the longest run will be determined by the location of the Hydraulic Control unit, not the master cylinder. (2 lines will go from the master to the HCU, then 1 to each of the wheels). On cars without ABS, the lines from the master will go through proportioning valve(s) then to each wheel.
You may also consider buying/borrowing/renting a "power bleeder" that you use to pressurize the master instead pumping the pedal. They make the job much easier.