Go to the website of the airport where you are changing planes. Almost every airport has its own website. If the airport does not have a website, it may be so small that navigating the airport will be easy.
Find a map of the airport and print it out. This is useful if you are changing terminals when you are changing airlines. Flight attendants may announce gates for connecting flights, but they only do so for flights on their airlines.
Bring the phone number for each airline with you. As soon as you land and the flight attendant announces that it is safe to use your cellphone, call the airline and get the gate number for your connecting flight.
Use the time while you wait to get off the plane to map out the quickest route to your next flight.
Research later flight options so if you are delayed and miss a connecting flight, you know what flight to request.