Change ignition switch on a 1995 bmw 325i - 1995 BMW 3 Series

In theory, if you poke a stiff wire or small drill bit into the hole in the face of the key lock, and rotate the lock to about where the second click should be, you can press the wire in and force back the spring-loaded latch and release the lock. This works perfectly with a brand new lock and housing. Unfortunately, most of us end up removing and replacing the lock AND the housing because getting the lock cylinder out of the housing when it is 15 years old is nearly impossible.

Assuming that your attempts to pull the lock out fail: First, disconnect the battery, wait a few minutes, then remove the screws from the back of the steering wheel and take out the air bag. Then remove the center nut and pull off the steering wheel. You may need to have a helper tap on the steering shaft while you pull up on the steering wheel to get it to break loose. Make note of the locations and orientations of the two bushing rings as you take it apart. Be careful with the electrical connections. Then remove the plastic shroud from the steering column. This shroud will be easier to get off than it is to put back on. Loosen the set screws that clamp the electrical part of the ignition switch to the end of the lock mechanism.
The lock housing is attached to the top of the steering column with security bolts. A dremel tool works well to cut slots in the security bolts. Then a short straight blade screwdriver bit turned with a small ratcheting box end wrench is the easiest way to unscrew the security bolts.

You will probably want a new key to go with your new lock because the key is probably pretty worn as well.

Be sure to lube your top steering shaft bearings while you have the housing off.

A short piece of 3/4" PVC pipe pressed down by the steering shaft nut is the best way to put the snap ring back in its notch in the steering shaft
Good luck! You are not alone. Everyone who owns an e36 has to replace their ignition lock sooner or later. The worst part is the cost of the parts, which are available only from the dealer.