Look for a minimum 2-hour layover for all international connections; ideally, your layover is closer to 3 hours. This helps insure against complications from delays (ex: missed connections) and increases the likelihood that your checked luggage makes it to your destination on time!
Whenever possible, book one ticket for the whole trip. For example, book your flight between home and your destination with one carrier (ex: Delta, American, United, etc.) rather than booking different flights with different carriers.
Book the fewest connections possible, even if it's a little more expensive.
If budget allows, consider upgrading to Premium Economy or even Business Class. These more spacious seats can help reduce the effects of jetlag tremendously!
After booking your flight, see if the airline offers discounted options for cabin upgrades – especially for overnight flights!
For international flights arriving at your final destination before 9am, consider booking a hotel room the night before to guarantee immediate check-in.
When taking an overnight flight, see if you can find a flight that arrives at your final destination sometime around mid-to-late afternoon (if possible). That way you can go through the entry process (see below), enjoy your transfer to the hotel, freshen up, grab dinner, and pass out. This helps offset jetlag and sets you up for success for the rest of your journey!