I’m a self published author (sole proprietor) with very few self employment expenses. I am wondering if the standard deduction is an option for me and how to apply it?

Your income and business expenses and the choice of a standard deduction or itemizing are not related. You take the standard deduction unless you have more in itemized deductions. TurboTax will make the correct choice for you. 

Don't confuse itemized deductions on schedule A with your business expenses/deductions on schedule C. They are separate. For Schedule A personal deductions, you get to take your itemized deductions or the standard deduction, whichever is larger.  Itemized deductions are things like Medical, Gifts to Charity, State Income Taxes Paid, Mortgage Interest, Property Taxes, Car Registration fees, etc.

You get to take both,  your business expenses AND the Standard Deduction (or your personal Itemized Deductions).  And you have to enter your business expenses.  Be aware, if you have self employment income you can get in trouble for not reporting all your expenses to qualify for the EIC.