No extension, the file is named ".asoundrc" and it's in your home directory. If it's not there, just create it. The dot at the beginning means it's a hidden file.

By the way, it would be easier for us if you're a bit more informative. Are you having difficulty locating the file? Or have you edited it already? Did it work? etc. etc.

it's not there, and how exactly would I create this file?

With any text editor of your choosing. Just save the file as .asoundrc

I put that code in .asoundrc and it didn't work =\

Well, sorry about that. Then delete it so that it doesn't mess other things up.

It looks like your card with codec ALC259 is not yet supported by current alsa-driver which is used in your kernel. You should search internet for your specific card (or vendor) and to see how manually it can be configured. You may also want to try to pass various options to the module when it is loaded. Here is a reference for various ones: http://alsa.opensrc.org/Hda.

how do I know which module to use?

Is there an alternate to alsa?

There are some other audio systems (the old OSS, the new OSS4, Jack and Pulseaudio) but some of these run on top of ALSA and the others don't have hardware support as broad as ALSA's. So I'd say it would be futile to switch to another audio server to fix your issue. You will probably need to wait until ALSA releases updated drivers supporting your card.

Well, it worked in Ubuntu so why wouldn't it work now?

ALC259 isn't listed in /usr/src/linux-2.6.33.4/Documentation/sound/alsa/HD-Audio-Models.txt (the model options for the snd-hda-intel module included with kernel 2.6.33.4). It doesn't appear to be listed in the docs for more recent kernel versions either. It has been supported by ALSA since version 1.0.21 (Slackware 13.1 is on 1.0.23 of alsa-lib and alsa-utils but sticks with the alsa support in the kernel instead of shipping with alsa-driver). You can try upgrading the kernel to see if you can get better support, but I'm not sure if that will help in this case. Post the output of
And perhaps post a screenshot of alsamixer with the capture settings displayed (Tab switches between Playback/Capture/All -- switch to Capture or All and take a screenshot).

There is ALC269 however, and 259/269 seem to be listed together in several places (I mean Google ). Maybe some options to modprobe might fix it?

bash-4.1$ arecord -l
**** List of CAPTURE Hardware Devices ****
card 0: Intel [HDA Intel], device 0: ALC259 Analog [ALC259 Analog]
Subdevices: 1/1
Subdevice #0: subdevice #0
bash-4.1$ ls -l /dev/snd/*c
crw-rw----+ 1 root audio 116, 6 2011-04-19 14:04 /dev/snd/pcmC0D0c
bash-4.1$

That output looks fine -- you only have one recording device so there's no chance for confusion due to multiple devices or subdevices. Make sure your user is in the audio group, make sure alsamixer is setup properly (still no screenshot so I can't verify that for you), possibly try passing options to snd-hda-intel based on the ALC269 chipset as Ilgar suggests, or try upgrading your kernel. I can't think of anything else to do. Possible model options for 269:

For 2.6.33.4:
For the latest kernel:

How do I add myself to audio?

Nano /etc/group/

I see:
audio:x:17:
that's all. Any suggestions?