No worries, that's what we're here for, to alleviate the confusion
Recompiling your kernel means to get the new source from www.kernel.org
Which source? Well that's up to you, it's your system, and it's for you to decide how stable you want to go. 2.4.20 is the current most stable kernel, however the 2.5.x series does come with the ALSA patches already applied. You take your pick, but my suggestion is the 2.4.20
From there, you normally download kernel sources into /usr/src then you untar them:
tar xvzf kernel-version
and enter the directory that is created:
Then you have 3 choices, if you want to go ultra hard corps, use make config, if you are a little more apprehensive, go make menuconfig (requires ncurses) if you are an X kinda guy/girl go into the directory while in X and make xconfig.
From there follow one of the thousands of tutorials/threads on compiling a kernel. Main thing you want to watch for is compiling soundcore as module. As for your specific driver (the via_82xx) you can compile that into the kernel or module as was mentioned above. At that point you can (hopefully) simply do a modprobe for your audio module: modprobe via_82xx OR you can compile ALSA (watch for errors from the ALSA programs) against your existing kernel. How? Well you will need to symlink your existing kernel version to /usr/src/linux
Well if you downloaded linux-2.4.20 then you would symlink /usr/src/linux to /usr/src/linux-2.4.20 (*The directory, not the tar.gz file) like so:
ln -sf /usr/src/linux-2.4.20 /usr/src/linux
Then compile your ALSA drivers according to the page over at ALSA's website.