Ske-Bum is basically right, but I think he is a little too pessimistic about toy GPS units. Most of them have WAAS correction for operation in the US, which improves the accuracy to about 3 meters. And the specified 10 meter accuracy is specified as 95%, so its something like a 2 or 3 sigma number, meaning most of the time you are quite a bit better.
I can't find specs on how many channels the receiver in my Garmin eTrex Vista hcx actually uses, but the satellite status page shows it tracking more than 3 -- does it actually use the full constellation, I don't know.
I don't know what hand-held military units are like. Are they any different from consumer handhelds?
The high end GPS receivers built into navigation units play a lot of tricks to get better accuracy and resolution, some even track phase changes as well as time differences. And for ultimate accuracy, you can do differential gps where the Coast Guard stations rebroadcast correction terms (based on the GPS signals they get at a fixed, surveyed site).
I did actually use my GPS on the hill once. At Solitude we came out of the woods to the back-to-the-base feeder trail at the bottom of Honeycomb canyon, and my directionally-challenged self wasn't sure whether to go left or right. The pitch at that spot was level enough that I couldn't be sure which way was downhill. So I got out the GPS and checked. That was the only time I've actually used it, as opposed to leaving it in my pack and downloading the logs at the end of the day. (Admittedly, getting out the trail map and thinking for a minute would have given the same result.)