Export the dialogue track for your animation to a file format that you'll have easily accessible on your computer. Listen carefully to the audio while keeping an eye on the timing, and make notes about what is said when.
Record video of yourself reading from the script. Exaggerate your mouth movements as much as you can without making the speech unnatural. Export the video to a computer file to use as a reference for your animation. Use a mirror to examine any movements that aren't clear on the video.
Keep your notes about the dialogue timing next to your keyboard and keep the audio file open. Animate the key frames of the most notable mouth movements at points coinciding with the timing on your audio recording. Create a static mouth position for times when characters are not speaking.