Massively has word that All Points Bulletin will feature audio advertisements over the game's VOIP channel, with an option of paying a premium to make them go away. They link to this forum post explaining how this works:

You will receive a short audio ad once every 3 hours. HOWEVER ads will only be heard when first entering a district.

So for example:

1) You start up the game and enter the social district.
2) You will hear a short audio ad.
3 You stay in social for 2 hours and then switch to an action district.
4) Upon entering the action district you will NOT hear an ad.
5) You play in the action district for 5 hours and do not hear any ads.
6) You exit the game.
7) You start up the game at a later time and enter a district.
8) You will hear a short audio ad.