It also depends on whether it is an on or off road duathlon. For road, if you are serious about getting a good time, shoes are already clipped into pedals so you run into transition, take off your running shoes and run barefoot to a line where you are allowed to mount the bike. You can then slip into the bike shoes whilst pedalling, some really keen types have an elastic band to keep the pedals horizontal, its hooked from the pedal to the rear skewer. When coming back from the cycle, you have to dismount before a line which you do by doing a cyclocross dismount without shoes, then run barefoot into transition and put on your running shoes again. This, if done properly, can save 2 or more minutes which is a long time on a bike.
Oh and don’t forget, the first thing you do when getting to the bike is put your helmet on and buckle it up, you can be disqualified for touching your bike without a helmet on, its also the last thing you take off before the final run.