There is an Import button on the Activities page, but it doesn't offer exactly the same functionality. If you want to upload workouts from your fitness device, you are expected to install Garmin Express. Instructions for doing so can be found on the Garmin Connect home page. Just click the Get Started button and follow the instructions. Note that this isn't mentioned anywhere, but you should uninstall the ANT Agent and Garmin Communicator Plugin before installing Garmin Express.
