Event number one is Mae Tuck beginning her travels to the small town of Treegap. She only makes the trip once every ten years, and she makes the trip in order to meet her two sons, Miles and Jesse.
Event number two is Winnie Foster losing her patience and deciding to think about running away.
Event number three is a strange man arriving at the Foster's front yard. He claims to be looking for somebody, and he won't elaborate.
All three of those seemingly disconnected events are indeed connected. The stranger turns out to be the man in the yellow suit, and he is looking for the Tuck family. He suspects that they are immortal, and he wants to find out their secret. The day after meeting the man in the yellow suit is the day that Winnie decides to give running away a small test run. She goes in the forest, and she meets Jesse Tuck. Mae Tuck arrives shortly after with Miles, and the three Tucks "kidnap" Winnie. As the Tucks try to spirit themselves away, they pass the man in the yellow suit.
I suppose if I had to pick a physical item or person from the story that connects all three events, I would pick the entire Tuck family. The stranger wants to find this mysterious family, Winnie accidentally discovers the family, and the stranger follows Winnie and the escaping Tucks in order to learn their secret.