Android - How can I change the data usage cycle for Mobile data?

Changing the starting day for Mobile data is indeed non-obvious. You need to enable the mobile data connection (2G/3G) before the options are available:

TURN OFF WIFI First.

1. Enable Mobile data.
2. Exit the Data usage settings app.
3. Tap the spinner below the Set mobile data limit checkbox.
4. Tap Change cycle....
5. Change Date of each month (I prefer the first day of the month, 1)
6. Hit Set.
7. Undo Mobile data if necessary (e.g. if on Wi-Fi).

For me (CM 12.1), it is still confusing. You have to go under Settings, Data Usage and then:

1. make sure that both Data connection and Set mobile data limit toggles are ON
2. below them, there is range of dates dropdown, which you can choose to see data usage of previous months. Click on it, and you will get a list of previous periods.
3. now, you have to scroll all the way down through all periods (mine seems to go back all the way down to January 1970 !!!) - below the last one there will be Change cycle... option. Click it, and it will allow to change starting date.