Ship assist work is done night and day in all kinds of weather (below in Bremerhaven)
Berthing a deep sea vessel with three tugs involves four vessels with four crews and four masters, each of whom is individually responsible for the safety of his crew and vessel. The pilot coordinates the operations and is the only person involved who is able to communicate with all parties.
The site Master of Towing Vessel Forum has more on the accident on the Clyde: More Thoughts on the Clyde River Tragedy
The Tugster has some photos of two tugs turning a ship towards the sea in Turning Tabuk - This is the usual "U.S" method with the tugs made up on the sides.