As Joe Mama has implied, it does all depend on your sound card. In my experience, a patch cord from your headhone output on your amp to a line-in jack on your soundcard will work. You must be VERY careful not to overmodulate. ie, the headphone jack is volume control dependent ... it's really the same as a speaker jack because your headphones are really speakers ... So if you are turned up too loud, all you will get is noise. LOUD noise. Experiment. Start at a low volume and work your way up to what sounds good. Run AUTO Volume Control often at different output levels to get the best volume / least distortion return. Record in wav and convert later. I have spent hours and hours doing this. Get WavePurity
http://www.wavepurity.com/usa/usa/frame.htm and process out the crackles, clicks, pops, etc. from your records and hiss from your tapes. There is a free version. It does a good basic job on tapes and records that are already in pretty good shape.
Clean your tape heads with alcohol. Clean your records with a half & half mixture of denatured alcohol and distilled water. Spray it on and let it soak a few seconds. Don't get it on your labels. Use a soft bristled (preferably natural bristles) paint brush to work it into the grooves (round and round GENTLY). Use a SOFT, DUSTLESS cotton cloth (an old cloth diaper works best) to dry it (again, round and round GENTLY). Treat it just like you would your plastic eyeglasses if you wanted them to last for several years.
Some might say that this is rough treatment and it is. It is, however, better than letting fingerprints, dust and smoke (of any kind) eating up the plastic ... and it will.
Hope this helps.
CVIII