You can record with your phone's sound recorder app or any other microphone you have available. No need for high quality equipment.
Try to position your phone/mic so that your breath won't directly hit in the mic (air hitting the mic tends to cause line-obscuring noise).
I can eliminate steady noise (like a fan) later with a noise reduction pass, but if there are people talking in the background or audible traffic that could be a problem.
Record in one continuous take, and I'll edit out the bad parts (when I record 20 minutes of my own voice acting, I end up with 10 minutes or less of usable material -- that's normal). If you don't think you got the line quite right, repeat it until you like it before continuning to the next line. Following this process, it shouldn't take more than 15 minutes to do all your recording.
Leave long pauses wherever you like: it's easy for me to edit out a pause, whereas I can't edit a pause into a spot that doesn't have one. When you mess up a line, repeat from your last significant pause. With a long tongue-twister sentence, it can be a good idea to leave a long pause at a comma so that you can do the sentence a piece at a time and messing up the end won't make you restart from the beginning of the sentence.
Start any time, don't wait for word from me. When you're done, email the recording to email@example.com in any compressed format -- preferably all in one file.
Please try to get it done within a week of signing up, or leave it open to others until you'll have time.
I may ask for a few retakes later, possibly much later when I've received everyone's lines and had a chance to hear how they mesh.