I purchased a business on 12/26/18, the transfer of the business didn't occur until 1/1/19. How do I account for this in 2018 on my personal taxes?
Since the business really wasn't yours to run in 2018, you don't have to enter it on your 2018 return.
If you will be running it as a sole proprietor you will report the income and expenses on a Schedule C in your 2019 return. To do this you will need either TurboTax Self-Employed (online) or TurboTax Home & Business (CD/download).