When someone puts through someone who is making a telephone call, they make the connection that allows the telephone call to take place. The operator will put you through He asked to be put through to Charley Lunn. = connect
If someone puts you through an unpleasant experience, they make you experience it. She wouldn't want to put them through the ordeal of a huge ceremony
pursue to a conclusion or bring to a successful issue; "Did he go through with the treatment?"; "He implemented a new economic plan"; "She followed up his recommendations with a written proposal"