An overwhelming decision is whether to take night time or day time flights. There are pros and cons for each, but it changes everything. This is the overwhelming factor that will affect how the flight goes.
Secondly if as is common you have a long travel time to your main airport anyway, and if in any event the flight leaves early in the morning, you'll have to travel to the airport the night before all stay at the closest airport hotel, and then fly fresh.
Similarly if you happen to arrive late at your destination, take a night at that airport hotel instead of trying to travel on to your relatives or whatever the case is.
Thirdly if a long flight with a stopover, in fact have a stopover at a hotel midway rather than going straight through.
Sadly points 2 and 3 cost money of course, which is unfortunate. (The smart-ass answer to this whole uestion is unfortunately something like "bring your au pair!" :/ )
All the other parents have made all the great suggestions, own seat, book "crib" seat up the front of the section, Benadryl or similar, nursing pillow, and generally try to relax as much as humanly possible. All human beings love small human beings, so you'll be surrounded by people oohing and aahhing, which is your natural right as a mom of a new child, so just enjoy it. Culturally if you fly say Thai Airlines when pregnant or with a small child, you'll be surrounded by waves of love from the crew!