There are those who would say that putting your amp next to your microphone is the BEST way to do it (depending on the mic and the amp). Just because it "seems" amateur doesn't mean it is--most guitars are recorded this way--and sometimes with cheap(ish) microphones (
http://www.sweetwater.com/store/detail/SM57/).
If you absolutely MUST go direct you'll want to get some kind of pre-amp ... and the AUX from your amp would probably work fine going into the LINE-IN of a cheap soundcard as long as the AUX on your amp has a pre-amp or can send post-gain. If you connect it to the LINE-IN on your soundcard and you get no signal then try connecting to the MICROPHONE IN. Consult your owner's manual on the amp for whether your AUX is pre or post gain. Always keep the volume LOW when you are experimenting.
But what quality are you looking for? If you don't care about quality you can use your current sound card (if it has a line-in) OR a cheap mic pointed at your amp and get
Audacity (free sound editor).
For better quality get a firewire (or USB) sound card:
http://www.m-audio.com/products/en_u...Solo-main.html
http://www.presonus.com/products/Det...px?ProductId=4
http://www.rolandus.com/products/pro...x?ParentId=114
Most of the soundcards listed above have decent pre-amps so you can bypass your amp altogether.
If you are looking to do multi-track recording you'll need to do a search. There are some free ones out there ... and everyone has their own opinion on what's the "best" editor. Personally, I use Sonar PE (
http://cakewalk.com/Products/SONAR/English/default.asp). But ultimately it is what YOU feel you can afford and what you are comfortable with. THEY ALL DO THE SAME THING and generally sound the same (the sound quality is mostly dependent on your signal chain NOT the software).