Here is how :
First of all, you cannot e-file your return. However, you can still use the TurboTax program to prepare your tax return and required forms. After completion, print them out.
Secondly, complete a Form W-7 and gather all the required documents. See https://www.irs.gov/Individuals/General-ITIN-Information.
Then, attach the printed return and required forms to the form W-7 along with the required documents and submit everything to the IRS Austin location in Texas by mail. ( see above link)
This bit me in the behind. Make sure to cross the checkbox for "Credit for other dependents" once you print out the 1040 form. TurboTax will not check that box if no ITIN/SSN is provided.
My dependent's name was there on the printed form but no checkboxes were ticked, and I got a notice CP567 from the IRS that they rejected the application because "listed as a dependent on an attached U.S. federal income tax return, but were not claimed for any allowable tax benefit."
Hopefully this will save others in the future some time.