If you are actually running your own business you can do it on Schedule C along with the appropriate depreciation schedule.
If you are just using the vehicle in the business of your employer you use Form 2106 Employee Business Expenses along with the appropriate depreciation schedule.
Keep a daily mileage log showing odometer readings and mileage for the business use. Understand that you don't get a deduction for going to work and coming home.
If you aren't using the vehicle too often it's less complicated to just take the business mileage allowance.
Above would apply to 2018.
Since December 31 2017 was a Sunday, you would likely have no business use for that one day, effectively giving you a deduction of zero.
Example: Purchase price $5000. Placed in service December 31, 2017. 5 year straight line depreciation (for illustration purposes). $1000 per year depreciation, adjusted by the percentage of business use. Business use for 2017 = zero. Ergo, no deduction for depreciation for 2017.
Now let's say you use the car 20% of the time in 2018. That gives you a $200 deduction for the second year. You've wasted the first year but putting the vehicle into service on December 31, 1017.
It would make more sense to place the vehicle into service on January 2, 2018, the first workday of 2018, and get the full 5 years depreciation.
You'll have to run your scenarios to see which works out better for you, depreciation and expenses or the mileage allowance. Keep proper mileage records and expense receipts and figure out which way to go at the end of 2018.
A tax attorney participates here and may have additional comments.
The IRS website has a variety of publications and tax topics on the subject.
