DO NOT give your baby any sleep or reading medications such as Benadryl if they are under age 2 without strict instructions from your doctor. These medications can be very harmful to your baby if not properly administered.
If possible, keep your baby awake for the few hours prior to the plane ride as long as your baby is not cranky or fussy because they don’t get their nap. This way he/she will most likely sleep for a good portion of the plane ride.
Avoid large amounts of food or milk prior to the plane ride. The change in cabin pressure can upset a baby’s tummy and they are more likely to feel nauseated and vomit.
If your baby is old enough to walk and explore, I highly recommend buying them their own seat. Even though infants under age 2 can fly free by sitting in a lap, it will be more comfortable for you and them if they have their own seat.
Make sure to pack double of everything your baby likes. First time travel can be stressful for a baby and they may want more of one thing than they usually do.
During takeoff and landing, the cabin pressure will change. You can place silicone ear plugs and/or bring something for your baby to suck on (pacifier, candy, etc.). The constant swallowing will allow pressure release for their ears.