Don't know what level you are at, but here is some of the basics, there may be some other options you can use too, this is how I do it:
Start off by getting a dummy number to test with
In Call Manager build a Call Handler that forwards your number to voice mail.
In Unity build a System Call Handler
Within the call handler
edit/transfer rules - Standard - transfer calls to greeting option
Edit/Caller Input - see keys caller would press select on the left side. To transfer to an extension select Call Action and enter the number. To use nested Call Handlers, you can select Call Handler, choose a PREVIOUSLY BUILT call handler and select Attempt transfer
Continue down the list of options you want until complete.
Edit/call handler owners - here you need to add all the users that will have rights to change the greeting on this call handler by clicking add user and finding them using their voice mail user name.
Save.
Using your Cisco Unity Connection Greeting Administrator, you can access this set up and record your greeting(s)
Test
When it works to your liking, you can substitute your real number for the test number and you should be good to go.
This is just very basic, but hopefully will set you in the right direction.