Recording off net

Hi There. I am trying to learn to play the clarinet. What I have been doing is playing music, religious, on different sites on the net and recording using a microphone next to a speaker using Audacity- then playing to the playback. But I need two computers to do this. Can I record straight from the net onto Audacity? It would greatly help my training if one could help me please.

Yes, but the process changes a lot with your equipment.