Part II, using a multimeter:
It's pretty easy. I'll start simple, just ignore this if it's familiar.
Continuity is a path that electricity can follow. All parts of the car are wired from the battery, through a fuse most times, then through a switch, relay, etc, then to the thing that does the work, then off to the car chassis somewhere. That last point is called a ground. The other wires are usually called positives or the 'hot' side if it's a live terminal like the starter.
The multimeter will have two probes and a dial or switch to change functions. Most have nine or more tests you can do. I usually only use three functions...Volts DC, Ohms (resistance) and continuity. You might have to switch the probes into different sockets for different tests. Read the instructions, it'll serve you well.
Now that we're over that, you'll want to test five wires. Use the multimeter (hereafter shortened to DMM) in continuity mode to test the ground side of each socket. BMW usually makes their ground wires brown. Other cars use black or green. Touch one probe to each socket wire, hold the other end to a bit of unpainted metal under the hood. There's a ground strap under the hood that's good for this. You should get continuity from the ground side and no continuity (or infinite) from the positive side. The front signal has three to test...one ground (the shell of the socket), the parking light terminal and the turn signal terminal.