Generally your pediatrician will advise avoiding a plane for the first few months (maybe as long as 6 months) unless you really need to travel. Planes are full of germs and you want to give your child time to build up an immune system. Obviously lots of folks do travel earlier and things work out, but I think a few months also gives you time to learn your baby's particulars and get used to moving around with all the stuff (stroller, diaper bag, etc).

We did our first flights right at 6 months LAX-ATL, ATL-IAD, and IAD-LAX. Things worked out so well that we did LAX-BKK (and then BKK-HKT and HKT-BKK-ICN-NRT-LAX) at 10 months. At 17.5 hours I think LAX-BKK was one of the longest flights on the planet at the time. We had 2 J seats with my son as a lap infant. Only issue was about 30 minutes when he woke up in the middle of the flight a little fussy - but was eventually able to distract him with the IFE remote. The 2.5 weeks in Thailand were great and except for Thailand not being that handicap friendly, which means not very stroller friendly, it was relatively easy traveling with an infant. We are still traveling long distances with our 3 year old (just got back from South Africa, Russia last summer, Italy a year ago) but it definitely gets more challenging as he gets older. Pencil in 6 months to 15 months as your sweet spot for travel.