How to clean up spilled paint on carpet?
So I bought some cheap carpet cleaner from the local grocery store and started dabbing.  With a rag soaked in cold water (my roommate also used a sponge, which may actually work better), I made sure to keep the carpet area wet.  I spent about 2 hours dabbing at the carpet, spraying the carpet cleaner every so often.  After a couple of dabs, I could tell the rag wouldn't pick up any more of the wet paint, so I would carry it to the sink, wring it out, and start dabbing again.

This seemed to work, for the most part!  The stain is hardly noticeable, and is still getting better as I continue to spray and dab when I have time.  It may be a little more work than expected, but it's better than replacing the carpet.

Some tips:


Make sure the paint stays wet in the beginning.  You want the rag to soak it up, and it won't absorb the paint if the paint is dry.
Try not to scrub too hard.  When I tried scrubbing, the paint would spread outside of the original drop zone.  Dabbing is better.
Don't leave a paint can on the carpet.  Ever.