Yes, I know how, I do it every day.
The patch:
Go into System preferences / Sound
Set the sound output to Line Out and the Sound In should be set to your sound in card.
Patch the Line out, computer, mono or stereo, to Line in on your sound card for Logic.
Method:
Select an Audio Track and start Rec. Highlight you internet window and press play.
It makes it easier if you can get both Logic Arrange window and your Browser window open on the screen at the same time.
I record talk back interviews and stuff like that. I also Capture video off youtube and TV Channels but I use SnapzPro instead.
With both Logic and SnapzPro you can capture or record anything from the net.
If you have a problem with this, come back with a post and I will try and explain it better but it is so simple.
David.