Corten steel is delivered un-weathered, as grey/blue steel. This is so that the steel can develop its rust coating on site, where it will develop evenly. The rusting process is a result of exposing the steel to wet and dry cycles, which naturally allow the oxide coating to develop.
To speed up the weathering process, you can use a variety of methods. The most common method is to use a saltwater solution, which can be sprayed onto the steel using an old spray bottle. This will speed up the rusting process, and the steel will develop its protective oxide coating much quicker. Care should be taken to evenly spray the steel, otherwise the rusting process may be uneven.
The benefit of allowing the steel to rust naturally is that it develops an even finish, and is a direct result of the weather patterns it is exposed to.