Observing Assistants (OAs)
The actual operation of the observatory is done by the OAs and observers. As a result, the OAs work closely with the observers during the night. The SA's responsibility is usually centered around the instrument operation and troubleshooting.
There are several areas where the OAs have particular expertise, but where they or the observers might ask for your input:
Target Acquisition
Depending on the instrument, the OAs will be heavily involved in Target Acquisition. As a result, they are usually very good at identifying the target among the star pattern in the guider. If the target is quite challenging to identify, the observer should have prepared finder charts. If there is difficulty acquiring, you might join in to help identify the correct target, but for the most part this will fall to the OAs and observer.
Focusing
The OAs are primarily responsible for Focusing the telescope using either MIRA or autofoc. They will almost always perform focus as one of the first activities of the night.
Performing additional focus runs during the night may be useful. The observer is the one who has to decide whether the time spent on focusing is worth the benefit, so they will likely ask for advice on this. Use your personal experience in advising them, but keep in mind that the OAs are very familiar with how the focus behaves through the night as conditions change, so I almost always suggest that the observer consult the OAs.
Safety
The OAs have primary responsibility for the safety of personnel and equipment at night. They use various rules and rules of thumb to make safety determinations on decisions like opening and closing or abandoning the summit. They are also usually in contact with other observatories regarding these decisions.
As the SA, I would defer to them on all safety decisions and I would never pressure them to reverse a decision to close or abandon the summit for safety reasons. Of course, if you see a possible safety problem which they might not be aware of (e.g. a bank of fog approaching on the cameras), you should make them aware of it.