AVR-Chat

>
>What filtering is necessary?  I assume a pretty big electrolytic on
>the 13v side ( and maybe a tantalum or something?), and something
>else on the other side.  On the output side I have seen 2 caps on
>some schematics, but the sizes and types were not listed.

Avoid tantalums.

You have bigger problems.
Have you checked the max current rating and max heat dissipation 
ratings for the regulator?

Also, the LM78XX series is not designed to run from vehicle power.
National makes a few that are though, and it won't be a painful change.

>I am sure this is a problem which is well known and solved for this
>application, so it might be easy to answer.  What specific types and
>sizes of caps are usually recommended?

0.1uF on input and output, located as close to the reg as possible, 
to stop oscillation.
You will need to add electrolytics on the input and output as 
required by the circuit, but they do not take the place of the 0.1 caps.
You also need a reverse-biased diode across the regulator's input and 
output, to prevent destruction of the reg, if there is a short on the 
input side.