I haven't flown with my Chi, but did with my last dog. Different airlines have slightly different rules, so call if you have any questions. Airports seem consistent in requiring pets to stay in their carriers, and they must stay enclosed on the plane, so be sure your dog is happy and comfortable with its carrier. Some airports have pet potty areas after you go through security, so look into that too.
In general, do what research you can (as you have already started) and do your best to follow the rules. Bending or breaking the rules does nothing but make all those traveling with pets look bad, which may lead to us being less welcome in the future.
First time Chihuahua owner with many years of dog experience!