Which model phone do you have? For the CL82509 and related DECT 6.0, you need to set the outgoing message from the handset when the answering machine is on. (It can be turned on from the handset).
For the outgoing message: with the handset in Idle mode, press Menu/Select. Use the up (Dir) and down (CID) arrows to highlight Ans Sys Setup. Then press Menu/Select. Use the same arrow keys to select Announcement and press Menu/Select again. Press 7 to record a new announcement. At the tone, speak your message clearly then press 5 when you have ended the message. The message will play back.
This model's manual is available here: http://att.vtp-media.com/ecp/documents/product_Product/132/UserManual/5995/cl82509_manual_USA_i6.pdf
. See page 15 to set the answering system outgoing message. (This is different than Voicemail. To set up Voicemail, you will need to see your telephone provider's documentation.)
Most AT&T phone manuals are available here: http://telephones.att.com/att/index.cfm/product-support/manuals/
I hope this helps.