How can I get local sub-channels with DIRECTV?

You don't, DTV doesn't have the capacity to broadcast the thousands of sub channels.

Use an antenna, either indoors or outdoors type

DIRECTV doesn't have enough satellite capacity to broadcast all of these sub-channels like BUZZR or ME TV for example. If you have an older receiver that supports the AM21 (n) then you can use the receiver and remote and record these channels as well. But, if you don't, just use an indoor or outdoor antenna and adjust it until the strength of the RF channel is strong. I used to do antenna installations a while back so feel free to ask questions.

If you are in one of the markets they serve, you can use locast to get the subchannels.

@TexasBrit and just for additional info on the AM21, does it work when not connected to the satellite? I wanted to bring my HR24-100 on a camping trip and watch the local channels with the AM21 without having to be connected to the satellite. Thanks for your input.

Up to a point, the receiver has to get the authorization code from the satellites periodically so it doesn't shut down, no one knows how long the code last.