Like most modern men, I didn't have much of a clue of what to do when I found myself holding my newborn daughter. I was more focused on the mama. But within a few days it was apparent that mama was tired as he**. I invested a lot of time figuring out how to put our little girl to sleep. At first this was to support my wife, but in time it became a treasured source of intimacy with my daughter. Sleep. And what's more - the methods I developed for putting our daughter to sleep (which didn't involve any breasts), later became vital habits that even my wife imitated as she weaned herself from the nighttime feedings that kept her in a near-insomnia state for the first two years of our daughter's life. In fact, during that weaning phase my daughter went to bed with me (because nighttime feeding with mama was too much of a distraction). Only later did mama join us in bed.
The Five S's are a good place for a young father to start soothing and putting your child to sleep: Swaddle, Side, Shush, Swing, Suck. Google it and you'll find tons of info. And remember - every child is different. It will take practice and perseverance. In time, you will develop a unique relationship with your child that not even his or her mother can replicate.
And whenever possible, try to sleep at the same time as your child.