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"
                }

      }

  pcm.defaultplayback{
          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

            }
    }

Execution

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