A well documented tip, rehashed here:
Using CUCM / Unity, how to send a caller directly to a voicemail box?
Assuming you have 4 digit extensions:
1. Create a voicemail profile in CUCM with a mask XXXX, and the pilot of the appropriate voicemail system.
2. Create a CTI Route Point.
3. Make the CTI Route Point DN extension #XXXX (or *XXXX, 37XXXX, etc.).
4. On the CTI Route Point DN, use the voicemail profile you just created.
5. Forward the CTI Route Point DN CFA to voicemail.
Dial #1234 and you will hear 1234's greeting.