Segregated Witness transactions work just like their legacy predecessors. There are a few global values like version and locktime. There is an array of inputs (UTXOs we want to spend) and an array of outputs (new UTXOs we want to create, for other people to spend in the future). There will also be an array of witnesses, one for each input. That is where signatures and scripts will go instead of the scriptSig.

The message serializations for all these components is documented here and here.