Influencing starts with understanding yourself and the effect you have on others. Sometimes we can get used to our own personal preference of communicating that we get stuck in a rut and we don't think about how it is being received. Sometimes we have to make a change in ourselves and see the world from another person's point of view in order to understand what is required for something to be a success; whether it's a working relationship, project or new business venture. We need to actively listen to people's concerns and not talk over them.
Link your request to an appealing and clear goal for the person you are trying to engage with; you need to have an understanding of them - do they think with their heart or their head? Connect with them emotionally to get them on board. Influencing is about being able to move things forward without pushing, forcing or telling others what to do.
When all else fails; read Dale Carnegie's How to Win Friends and Influence People.