I own a 1999 Chevy Cavalier with an auto transmission, and it has
begun lurching badly when it changes gears. Oddly, it only does this
once it has warmed up after some driving. It changes gears smoothly
when I first start driving it. I thought it might be just getting low
on transmission fluid, but I can't even find a place to add
transmission fluid under the hood. Does this sound like the whole
transmission is starting to go, or is it probably something smaller
(and less expensive to fix)? And if it's low transmission fluid, how
do I go about adding more fluid?

It sounds like you have some slippage, and it is starting to fail on
you.  So the answer to your question is yes.

To add more fluid to your transmission, you should look near the top
of your transmission case on the drivers side under the hood.  There
should be a fill hole via a round plug (sometimes red or blue).  You
may have to really look for it, because sometimes its really hidden
behind the wiring harness that runs through there, and its a pretty
busy area.

To check the level on it, you must get underneath the vehicle, locate
the engine oil pan, and look toward the driver site.  On the side
closet to the engine oil pan, near the transmission oil pan, you will
see a small 7/32" bolt.  This is the fill-level hole.  You check the
fluid level by warming your car up, and removing this bolt.  If fluid
starts seeping out, then the level is fine, if not, you must add more
fluid up top.

The whole thing can be an annoying process, and is much harder to do
than simply having a dipstick tube, and filling it through there. 
Hope this helps.

I finally found out the problem.

Although one guy at the GM dealer wanted $950 to replace the valve
body, it turned out to be just a faulty temperature control that was
affecting the transmission. They traced a wire and replaced a $25 part
("sensor
3.682") and it now runs perfectly. The labor jacked the cost of repair
(at the GM dealer) to $275. I ended up spending a lot more on renting
a replacement car while they took almost a week to fix the car. So the
price was relatively low, but if you have the same problem, try to
avoid renting a car in the process... just have them check and replace
the sensor.