It's not that difficult, but it does help to know what the options are. These options are pretty much age-related:
Clearly the choices are varied and depend largely on what your child (or children) is happy with.
Don't forget about situations like the weather (wind, rain, sun, heat and cold can all raise their own problems) and sleep. Your child will very likely be inclined to doze or sleep heavily in either a child seat or a bike trailer, so be prepared for a well-rested child at the end of your journey!
Think ahead if you're using a bike trailer, as they are up to a metre wide and won't fit through many obstacles put in place at the ends of cycle routes.
As for traffic, be confident but sensible. Almost everyone we've encountered on the roads of the UK (mainly), Spain and Italy have been exceptionally courteous and patient - yes, even the mad Italians! Try to wave drivers through if you can clearly see it's safe for them to overtake, but not if you would feel unstable doing so.