How do I record two channels at once on a DMR-EX773EB DVD Recorder

I cannot find on online manual for this model. If dual channel recording an actual specification for the model? If it really should be able to record two channels at once then it may be similar to the DishNetwork DVR. It has one input but internally splits and creates two different outputs for two different channels.
Check to see if there is a mode setting for single/dual. You will need to set it to "dual". The Dishnetwork DVR has what it calls TV1 and TV2. You can record to TV1 but cannot watch a different channel on TV1 while it is recording. You CAN however watch and record a different channel on TV2 while TV1 is recording. (and vice versa). You can also record two shows while watching other recorded shows.
I'm guessing that you may need to look for some recording options to be able to record two channels at once.