The quest walkthrough below is an example of one of the many "Kidnapping at [location]" quests you'll get from random settlers in one of your random workshops or settlements. The objectives are simply traveling to the indicated settlement, talking to the marked settler to start the quest, finding the kidnap victim in the marked location (and clearing enemies in the progress), and bringing (fast-traveling) the victim home. If the victim dies in any cause (hostile or friendly fire, or accidents), the quest will fail automatically.
Once you cleared the mission area, return to the settler who gave you the mission and talk to him/her to complete it. If ever the settler who gave you the mission is a provisioner or someone you assigned to establish Supply Lines, you have to wait for that NPC to arrive in one of the settlements he/she'll visit.
Upon arriving at the County Crossing settlement, the settler there may approach you and ask for your help. If you agreed to help him, this quest will trigger and the BADTFL Regional Office will be marked in your map. (Refer to the location's page for more details about the notable loots and points of interest)
Just take the shortest route available. Cross the bridge and head west. You'll encounter raiders along the way and some guarding the building's entrance. You'll find the hostage inside the prison cell further inside. There are two ways to reach him; one is through the office area (past the laser turret room) or the filing room. The area is overrun by raiders, including a named “boss” raider called Sparta. Kill them all and rescue the hostage. Before leaving, you can continue looting the other items.
Once you're done, report to the settler to complete the mission. You can also ask them to join the Minutemen. Examine the workbench in this area and you'll be able to use this settlement as well.