For installing ALSA from binary distro packages see ALSA Setup Guide. You can also choose to install the drivers from source (to make sure they fit your kernel) and install the libs, utilities etc. Debian users choosing to do this should run Kernel 2.6.
You don't have to do this though, there are binary packages available. XXX users: If you have a kernel from the 2.6series, ALSA is already included, so it's not necessary to do all these steps.
The stable drivers are more thoroughly tested; however the development drivers typically have newer hardware support. You should download the development drivers instead of the stable ones if that is the way you would like to go.
Of course, you need a sound card that is supported by ALSA. You can download the sources from the front page of the ALSA home page: To make module loading permanent, you have to add these lines to /etc/(for Debian users, this means you have to create a file with these lines in /etc/modutils and the do update-modules).
Reboot your computer and the newer ALSA modules will be used.
Remember that you may need to adjust your volume settings.
I am new to Linux but really love Elementary for its simplicity.
After noticing that my sound was quite poor in Elementary, compared to Windows 8.1, I have tried updating the sound drivers.