You hear "the art and science of project management." Though there is plenty of science around this, your question invokes the art with me.
1. Keep your eyes on the prize. Know the higher purpose of the project and who it benefits and how, and evangelize that.
2. Find your early adopters, and spend 1:1 time working through issues and insights with them. Interestingly, many early adopters are initially disguised as the harshest critics.
3. Make roles and expectations very clear, so people can operate with a fair amount of self-management (hear "don't baby sit them"). They should also know the roles and expectations of other teammates, so collaboration and shared responsibility can emerge. Read about Tuckman's model and what it takes to push the team into a "performing" state. It's relevant.
4. Give honest and frequent appraisals of performance. Make it conversational, not eventful. Be on the same side of issues. If they're struggling, figure out why and help them through the woods into the clear. You believe in them, right? They'll get that, and appreciate you for it.
5. Have a story-board, which is really just a Gantt chart on steroids, that can be blown up and placed in a prominent wall. Show progress. People are always pessimistic of big challenges before they've started. They are also typically surprised (and quite inspired) when they see how much the team is getting done in such a short time.
5. Weed. There are inevitably some antagonists, that won't play. They can be a cancer to the rest. Help them out of the project and into a better fitting job.
There's a few thoughts. Have fun. Get their hearts and their minds will follow.