Search this board and bimmerforums and there are a number of DIYs with pictures about replacing brake lines and bleeding. Two things I found priceless in doing this:
1. Motive pressure bleeder w/the correct cap to fit BMW master (mine came w/ bottles & tubes to collect the spent fluid)
2. Good set of metric flare wrenches
To change out the flex lines between the car body and caliper you'll have to take the caliper off the wheel (two 18mm front and 16mm? rear bolts). You can then either cut the flex line (since you're chaning it out) OR try getting a wrench on it to break the seize and then spin the caliper to undo the line. Not much brake fluid comes out so you can either let it drip into a pan while you undo the top part from the hard line at the body mount or plug it with something (I found a golf tee jammed in the cut hose worked fine). Good flare wrenches are worth their weight in gold undoing the body side connection (will make sense when you start messing around with it).
Bleeding with the pressure bleeder is fairly simple - read the directions, but main steps:
1. Use a clean turkey baster to suction out 1/2 or so of the old fluid from the master (not 100% necessary but speeds the process and doesn't waste as much of your new brake fluid)
2. Put a liter or so of fresh fluid in the bleeder, screw on the pump top and then connect the hose to the master cylinder
3. Pump up the bleeder to 15lb or so and check for leaks (have plenty of towels ready - brake fluid is nasty stuff to clean spills immediately
4. Attach a hose and catch bottle to the bleed screw on the caliper (which you've already put back on the rotor)
5. Open the bleed screw and wait for clean fluid/no bubbles to pass
6. Tighten bleed screw and move on - typically you do RR, LR, RF, LF (moving from farthest from master to closest last)
Hitting the caliper with a rubber malet can help get bubbles out (just don't go crazy). Don't let the bleeder bottle go dry or that will put air into the system and you'll have to start over. Note this method does not cycle the ABS unit - if you can find a board member who has the computer with DIS/GTI/whatever near you then you can do that part too. Also depending on the age of your e39 you may want to check the "in between" hoses that run from the ABS unit to the hard lines for the rear for cracks/wear. On my wife's 12yr old 530 they still looked ok, but after 110k miles next to the exhaust I changed those too.
Some real good advice here. I need some flare wrenches so I don't round off those nuts. Whomever last bled my clutch round that sucker so badly that I couldn't break it loose.
I did mine with the 2 man bleeding method(without a pressure bleeder) and it worked very well. I have a VERY solid brake pedal.
I didn't have to remove the calipers to change the brake lines connected to the caliper and I don't think most people remove them unless they are also changing out the pads. It was easy to do it while still on. It can sometimes be awkward but a simple few turns of the steering wheel can go a long way in opening up some space.
For sure use a rubber mallet to bang on the caliper while you bleed to dislodge any sticky bubbles in the caliper as noted above.
Don't have the bleeder valve open for too long. Open for a few seconds to bleed, then close it to get more pressure on the pedal bleed some more and repeat until you no longer see any bubbles but always check the reservoir and top it up when needed. You do not want to introduce any new air into the system as noted!
After you do the initial bleed, find an open stretch of road preferably wet or icy( to save your tires) and activate your abs this way and then perform another bleed for a rock solid pedal.
