Well, this is the second way to skin the cat.  Note that arecord ignores what went into the recording section of the config file specified below.  See the execution section for actually making a record or playing something.

Followed the instructions of OP in this post, more or less (as detailed below).  Note the extra information provided by the top post at this link.

For some reason, the space on the RPi's SD card filled up completely after following those instructions and messing with the results.  Not even enough space to run ls on a big directory.  Something I'd expect if I'd run arecord instead of aplay, and left it going indefinitely.

Log into the pi.
ssh pi@raspberrypi
Install a dependency (don't worry, it's small).
sudo apt-get install libasound2-plugins
Edit the ALSA config file, but first backup the original.
cp ~/.asoundrc ~/.asoundrc.bak
sudo nano ~/.asoundrc
Add the following to the file.
pcm.!default {
type asym
playback.pcm "defaultplayback"
capture.pcm "defaultrec"
hint{ show on
description "default play and rec koko"

pcm.defaultrec {
type plug
slave {
pcm "hw:1,0"
rate 48000
channels 2
format S16_LE
hint{ show on
description "default rec koko"


type rate
slave.pcm mix1
slave.rate 48000

#Intel(R) Core(TM)2 Duo CPU E7500 @ 2.93GHz:

#converter "samplerate_best" # perfect: 16%cpu, maybe overkill
#converter "samplerate_medium" # almost perfect: 6%cpu
#converter "samplerate" # good: 4%cpu, definitely usable
#converter "samplerate_linear" # bad: 2%cpu, way better than default wine resampler
#converter "samplerate_order" # very bad: 2%cpu, like the default wine resampler

converter "samplerate"

hint{ show on
description "default play koko"

pcm.mix1 {
type dmix
ipc_key 1024
slave {
pcm "hw:1,0"
rate 48000
periods 128
period_time 0
period_size 1024 # must be power of 2
buffer_size 65536



To play a file (of the proper format):
aplay file.wav
To record a file:
arecord -f cd file.wav
Read the aplay or arecord manual to see what's up with the -f cd thing.  Essentially, it's specifying the format the audio should be in.
man arecord