Thanks for the help, guys. It seems to be working now.
I tried it again, put the clamps around the negative wire from the battery ( it was easiest to reach), turned the meter to DC Amps 0-40, and it started giving out random numbers. I zeroed it, as suggested, and it started to read out the draw.
I believe the culprit is the car radio, which we saw going on and off by itself while the car was parked the other night. This AM, we had a dead battery (almost new battery, by the way). I measured the amp draw with the radio fuse pulled, and it was very minimal. When I put the fuse back in, with the radio off, it was pulling about 1 1/2 amps, which I think would account for the dead battery. I think I need a new radio!
Thanks very much. I knew you guys would come through!