I have a sinus infection. What sleeping techniques are there so that I don't get extreme dry mouth in the morning?

Biotene. The use of boiotene dry mouth system is advisable. The kit comes with a rinse, toothpaste and lozenges. Using a rinse is a very good idea before bed time as it coats the mouth and keeps it moist. Do not use alcohol containing rinses either.
Biotene Gel. The main way to prevent acute dry mouth is try to breathe with your mouth closed. During a sinus infection that can be difficult. Nasal sprays like afrin do well short term to help clear nasal passages to breathe. The other thing you can do is go to the drug store and pick up biotene gel. It is a product designed specifically for people with dry mouth to help keep tissues moist longer.