The simple answer...
Hi, Dave...I don't own an 880, but the simple response to your question would be that you go from a line-out on your 880, to the line-in on your soundcard. Depending on your soundcard, you might/should have some sort of line-in source...on my own soundcard, for example, I have a 1/8" stereo line-in. I'd go from the recording unit (880 in your case) to my soundcard's line-in, and record to my hard drive. If hard drive space is, or becomes, an issue...hard drives aren't all that expensive, and you could add a dedicated hard drive to your computer and have lots of space just for your music.
Some thoughts for you to consider anyway. Have a great day.
Julia