Out Of The Comfort Zone

Everyone wants to know how to have more influence. So many roles require cross team, cross functional, cross divisional or cross border coordination where the leader is accountable but has little formal authority over the resources that are needed. Or, if the leader does use formal authority, reactions are not usually very positive. What is the secret to influencing without using or having authority? How can you influence upwards? What if the influence is through virtual channels only?