Here are the general steps involved in replacing the vacuum pump on a 2004 BMW:
1. Remove the air intake hose.
2. Remove the serpentine belt.
3. Remove the vacuum pump mounting bracket.
4. Remove the vacuum pump.
5. Install the new vacuum pump.
6. Install the vacuum pump mounting bracket.
7. Install the serpentine belt.
8. Install the air intake hose.
*It's important to note that this is a general overview and the specific steps may vary depending on your exact BMW model. Additionally, it's important to follow the manufacturer's recommended procedures and safety guidelines when performing any repairs on your vehicle.