If your top priority is to minimize immediate Civilian casualties, simply do not start a war. Is it really as simple as that? Yes it is. Everything else will always be a compromise between short term and long term goals or inherently opposing goals like trying to achieve some military objectives at the same time.
If you are somewhat less willing to minimize Civilian casualties, do not attack populated centers, instead go around them and try to conquer less populated areas. Then ask Civilians to leave the populated areas and offer them free evacuation and even free food supply. Remember for example that "The use of starvation of the civilian population as a method of warfare is prohibited." (rule 53).
If your are still less willing to minimize Civilian casualties (but at least somewhat) think hard about which and how many forces to use. Remember that "Launching an attack which may be expected to cause incidental loss of civilian life, injury to civilians, damage to civilian objects, or a combination thereof, which would be excessive in relation to the concrete and direct military advantage anticipated, is prohibited." (see rule 14 "Proportionality in Attack" of International Humanitarian law).
So for example, long range artillery is known to be not very precise. If you think that their use is excessive in relation to the concrete and direct military advantage that you anticipate then don't do that. However, it may depend on your estimation of the expected casualties and military advantage, so kind of very subjective and in general always a compromise of the willingness to minimize Civilian casualties.
All of these considerations and more are outlined in the Geneva conventions, the Hague conventions, or other International conventions for example regarding the use of certain weapons (chemical, anti-personal).
What the rest of the world can do? Well, I think they already do a lot and I'm not sure that there is much more that effectively can be done short of directly taking part in this war. Donate to humanitarian organizations like "red cross" and continue to put pressure on Russia, use your political influence locally to support politicians that put that pressure on Russia to at the very least scale back attacks significantly if not cease firing immediately. China, India, ... are surely countries that could do more there in this regard. Most influence would actually have Russian civilians there, but it's unclear what the best ways would be to put pressure on their own government. I would say this could be its own question on this StackExchange.