You need to use a dmix PCM for you card as output.
If you type aplay -L | grep dmix
it'll show you a list of dmix devices. You can set one as the default if you create a file named .asoundrc
in your homefolder with the content:
pcm.!default {
type plug
slave.pcm "dmix:CARD=Set,DEV=0"
}
You of course replace the value of slave.pcm with your desired card name. I just gave one of mine as an example. The above default configuration also takes care of automatic conversion, via the plug
pcm, for different samplerates and formats to the settings the hardware is set up to use. Every program that use ALSA for output will read the above file, but you need to restart a program for changes to take effect.
If you enjoy audio production I'm sure you'll find some good use for Jack, but for audio mixing all you need is to use an ALSA dmix pcm for output.