My first riff I ended up recording the lines one at a time an inserting them into a track on Audacity according to time code, which was a huge pain in the ass and I would definitely not recommend it.
Since then I've been using/adapting the method Asbestos Bill posted
here I only use one computer, a USB headset for hearing the movie and one USB condenser microphone that any and all guests have to share (at least until I can afford to buy a second one) There is going to be some background noise to deal with, but here are a few tips to minimize it and remove as much as possible. These seem to work for me, but if anyone with more experience can add to or correct anything feel free.
1. Obviously if you can, turn off anything that'll make such noise. Turn off the heater/AC while recording, as well as any washers dryers dishwashers etc and make sure you tell anyone you might be sharing your house/apartment/flat/cardboard box with that you'll be recording and to keep it quiet. You'll still have some noise to deal with, like the fans on the computer you're using, but you can at least minimize it.
2. Set up the microphone(s) as far from the computer as you can while still being able to see everything you need to and reach the mouse/keyboard. (If you have wireless controls, this is the time) I end up putting the mic on top of my hamper, which is in turn put on top of a small table so it's just about head hight while standing. If you prefer to sit, make sure the chairs don't make squeak or creak noises. Stools would be optimal compared to office chairs.
3. If you can, make a makeshift soundproof box. Take the surface you're putting your microphone on and figure out how to surround it on all but one side with a box lined or covered with fabric, this'll absorb a lot of the sound in the room, except the sound coming from your direction. I experimented with this last night with good results, using a plastic crate and covering it with my jacket. Next time I set it up I'll try and get a picture as an example.
4. The first thing you should do with your audio file after recording is normalize it. Highlight the entire track and click normalize from the effects menu. (If you're not using Audacity there should be something similar to this, if not then look for something that says it will remove or fix "DC Offset" This will make sure your moments of silence will be centered on the zero line, making more seamless editing possible.
5. If there's still a lot of background noise, then highlight a section of just the noise and go to effects again. Click "Noise Removal" and in the menu click to get a "Noise Profile". Once that's done, highlight the whole track and go back to "Noise Removal". You can probably click OK and use the default removal settings and be happy with them, there's a preview button, but since your track is going to be long it doesn't give you much of a hint to what you're doing. You should probably listen to a long stretch of the file after doing this to see how much effect it had and if you're not happy click undo and try again.
I've been thinking about putting together a full guide for this, incorporating everything I use from other guides and personal experience into one resource (giving full credit where credit is due of course

) If I get around to it I'll post it here.