Some spacecraft dock with the International Space Station and others berth with the station.
Docking: The spacecraft can maneuver and attach to the station by itself. The Russian Soyuz and Progress vehicles can do this.
Berthing: An astronaut uses the station’s robotic arm to capture the spacecraft. Then Mission Control takes control from the ground and directs the arm to maneuver the spacecraft to the attachment site. This is the process for automated vehicles including Dragon (SpaceX), Cygnus (Northrop Grumman), HTV (Japan Aerospace Agency), and ATV (European Space Agency).