Soak with penetrating oil, wait a day or so.  Heat the lug nut with a torch,
if the current wheels on the vehicle are steel.  Wear safety goggles, lots
of people don't.  Try a commercial nut splitter, if there is room to get it
on there.  Grind off a side of the nut, with an electric grinder or a Dremel
and a lot of patience.  Then when you put some torque on it with a socket,
it should loosen up.  Some people prefer to go straight to the chisel stage.
Make sure that it is a sharp one.  Air chisel?

Once you get the nut off, and the drum if it is on the back, you should be
able to tap the stud out the back with a hammer.  Don't inadvertently hit
one of the other studs when you do this.

Earle

Have you rounded off the nut yet?  If not, then you just need to use
more force... I've found that I can put more torque on my lug nuts
with a T-handle lug wrench than my air powered impact wrench can exert
to remove the nut... If all else fails, put a cheater bar on your lug
wrench... If you still can't break it loose with a 4-6 ft cheater bar,
either you're a wimp or someone welded your lug nut to your rim...

testert555 did pass the time by typing:

Ah.. someone probably spun them on with an air wrench.
Never use an air wrench to torque lugnuts, always use a torque wrench.
It's especially important on disc brakes.

Mark the one that won't come off with a marker, put the other ones
back on.  Go to a local auto shop and ask if the mechanic could hit
that nut with an impact wrench.

What ever you do, don't lean on a lugnut wrench... if the bolt or the stud
goes you could wind up eating pavement.   A 3' breaker bar and six point
socket works for me on most.  Just remember where the bar is going to go
if it lets loose. :O

Hammer the old one out, lube up a new one, use the tire (or a thick bit
of pipe/washers, and lugnut to suck the new one in)  Not that hard, it
just depends on how bad the rust is.

#I got a new set of wheels/tires for my 91.  I was able to loosen all
#but 1 lug nut.
Put the other 4 back on.  Get them nice and *hand*tool* tight.

Did the cap come off the lug nut?  If it did, you now have a metric lug
nut.  17mm or 18mm, iirc.  If you still have the cap, you can use it to
"adapt" the metric lug nut back to a 3/4" one.  The problem is that the
sheet metal is kinda fragile and it only works once or twice before the
sheet metal tears.

#I've read lots of suggestions, but need to know, how do I proceed with
#doing the least damage?

Go to Sears and buy this or something equivalent to it:
http://www.sears.com/sr/javasr/product.do?cat=Mechanics+Tools&pid=00944816000

You can also use a flex head handle without the ratchet:
http://www.sears.com/sr/javasr/product.do?cat=Mechanics+Tools&pid=00944202000
I just find the ratchet is more useful overall...

You want the longer handle.  This way, you don't need a cheater bar.  

The flex head lets you have a bit more working room away from the
sidewall while still remaining fairly close to the lug nut.  The
problem with most tire irons is that it seems that half your effort is
being used to keep the tire iron from slipping off the lug nut and that
you can never get enough leverage.  Never mind most have cheapie
6-point sockets made out of pot metal.

Use a 12-point 3/4 inch socket (if your cap came off, then you will
need a 12-point 18mm (or was it 17mm?) socket).  

If the lug nut is totally stripped to hell, then you will need this:
http://www.sears.com/sr/javasr/product.do?cat=Hand+Tools%2C+General+Purpose&pid=
00952162000

Once you loosen the bad nut tiny bit, leave it on and loosen the other
nuts a tiny bit in a star pattern, then loosen the bad one again and
repeat.

If you have stock sheet-metal covered lug nuts, replace them with good
quality solid ones.

#What's involved with replacing the studs if it comes to that?
Front or rear?

/herb