The women in question, Estrella Benavides, says she doesn't actually hear the voice of God telling her to do something, but instead just gets a feeling of what He wants her to say. If we were in her shoes, we'd use that power to "feel" who God is going to have win the Superbowl, but that's just us. She's claiming freedom of speech and all that but the city council is saying it's a nuisance and coming up with all sorts of ordinances to try and put an end to it. She has, however, agreed to no longer broadcast messages out of a loud speaker she installed on her car.
The fun part of the story isn't necessarily her, but the reactions to her by her neighbors. All are unfaingly polite and try to go out of their way to say nice things about her, despite the fact that it's clear she's completely bat-shit crazy. It's almost a Borat-like thing where she presses the envelope on crazy and her neighbors are too worried about being impolite to really do something that they're probably all thinking deep down inside.
KTVU, which is where we got the image from, has a slide show of the craziness.