Update I have now upgraded to CyanogenMod 7 (based on Android 2.3). Please check this post for details. Steps are similar to what is mentioned here.
This post is about how I got CyanogenMod installed and running on the Motorola Milestone. More information on CyanogenMod can be found here or here. The Milestone port of CyanogenMod was made by nadlabak
Disclaimer
Proceeding further means you understand what you are doing. I am not responsible for any damages that might occur! This might also void your warranty. This worked for me.
Backup all important data
Data on the SD card like photos, music will not be affected. SMS messages, call logs and music playlists will be removed. If you have lots of messages, you could try one of the SMS Backup apps from the market, which will save all messages to GMail or SD card. It would be wise to check on a per-app basis to see if data is stored locally or in the cloud.
Flash vulnerable recovery.
Without this, remaining steps will not work! Please see this link for instructions.
Download androidiani-openrecovery
http://code.google.com/p/androidiani-openrecovery/downloads/list.
Current version: OpenRecovery-3_3.zip
Connect phone to computer
Use the USB cable and connect in mass-storage mode (Memory card access).
Extract OpenRecovery
Copy extracted folder to the root of SD card. You will have a folder called OpenRecovery and a zip file called update.zip

Download CyanogenMod for Milestone
http://code.google.com/p/cyanogenmod4milestone/downloads/.
Current version: update-cm-6.1.2-0.05-10.12.27-Milestone-signed.zip
Copy the zip file to sdcard/OpenRecovery/updates.
Google Apps
Google apps are not included in the CyanogenMod ROM. To get them, download HDPI version for CyanogenMod 6 from http://wiki.cyanogenmod.com/index.php?title=Latest_Version/Google_Apps.
Current version: gapps-hdpi-20101114-signed.zip

Flash CyanogenMod
Make sure the Phone is fully charged. Power off and start in recovery mode.
Press and hold the camera button and power on the phone. You will see a screen like the one below.

Press the volume up button and the camera button simultaneously to bring the recovery menu

Using the volume button, highlight the second option
apply sdcard:update.zip
Use the middle button on the d-pad of the hardware keyboard to select the highlighted option. This will launch the Androidiani OpenRecovery that was downloaded in the second step.
Using the volume keys, select the three wipe options below and apply them using the d-pad:
- Wipe Dalvik Cache
- Wipe Data / Factory Reset
- Wipe Cache Partition

Still in OpenRecovery, select Apply Update option and then select the
update-cm-6.1.2-0.05-10.12.27-Milestone-signed.zip
Confirm using the d-pad. Once that completes, use the Go Back menu option and choose Reboot system
You should now see the CyanogenMod logo when the phone boots.
Install Google Apps
Follow steps 1-4 of Flash CyanogenMod, click Apply Update and select gapps-hdpi-20101114-signed.zip
This will install Google apps and the procedure is now complete. You will need to sign in again to GMail, Facebook, Twitter and other services.
Some Screenshots
[slideshow]