There are two different approaches to producing Form 1099-MISC and accompaning Form 1096 Transmittal using TurboTax.
The simplest is to use the online service that is available called Quick Employer Forms which not only produces Form 1099-MISC but also W-2, 1099-INT and 1099-DIV.
The link to get you started is here, but realize that all your employee data for your 1099-MISC recipients will be stored online only.
As a purchaser of either TurboTax Business or Home&Business, you can use this link and sign in with the log-in used to either purchase the product or to register, or to access support.
Alternatively, you can do all Form 1099-MISC/1096 work, except printing, on your computer and then go online to QEF to electronically transmit the 1099-MISC Copy A& 1096 [note these forms require printing on red-inked forms which is why it makes sense to do online submittal]