OK, let me take a stab at this. ?
Your onboard card should be OK for recording. Obviously you'll need to plug your guitar into it (or amp, or amp modeler, pedal, whatever ? ) - into the Line In (Mic might do as well). You should be able to hear your playing through your speakers as is, but you might experience some latency. Basically you pluck a string and the sound coming through your speakers is delayed. To fix that you need ASIO drivers. That should fix the latency problem. Try the driver from
http://www.asio4all.com/ - if all goes well, it's a simple install and configuration ( RTFM ? )
Once that is all fixed you'll need some software. I've heard people using Audacity and such things, but considering it's free, why not go for Reaper (
http://www.reaper.fm/ ). Bit of a learning curve, but it's pretty easy to get some basic recording done.
I think that's it. My setup is similar (I just set it up about 20 minutes ago). Only difference is that I have a USB interface that doesn't need the ASIO drivers.
If I've missed anything, others can fill in ? Hope it helps, though.