For deducting vehicle business expenses from your business income, you have two options:
Deducting the actual expenses for your vehicle (depreciation, fuel, maintenance, etc.)
Taking the standard mileage deduction (57.5 cents per mile in 2020)
For most people that are using their vehicle for both business and personal travel, the standard mileage deduction is the easiest and best method. If you do this, you only need to keep track of how many of the miles you drive are related to the business.
The IRS wants you to have some sort of log that shows the miles that you drove for business. A paper log book is good, but an app works just as well. Photos of the dashboard are not necessary.
If you are taking the standard mileage deduction, you do not need to keep track of any maintenance records or fuel receipts; the only thing that matters is how many business miles you drove.
When you fill out your 2020 taxes next year, your business will be accounted for on Schedule C. On this form, you need to declare all the revenue (income) for your business. So if DoorDash ends up sending you $6000 in 2020, then $6000 is what will get entered at the top of Schedule C. DoorDash will also be giving you a 1099-NEC form that will show you exactly how much they sent you, and this amount will also be reported directly to the IRS. But you do not pay tax on this entire amount. On Schedule C you will also report any business expenses that you had in 2020. Mileage will be the biggest deduction, and there is a place on this form to enter in the number of miles you are claiming. If you had to purchase any other supplies for your business (maybe insulated bags?), you can also claim those expenses.
Revenue minus Expenses is your business profit, and this will be calculated on Schedule C. If your total business revenue was $6000, and you drove 10,000 miles to earn it, your business profit would be only $250. It also would mean that you were drastically underpaid. :)
This business profit is what determines how much tax you will pay. There are two types of tax on this profit: income tax and self-employment tax. For income tax, the profit will get added to any other income that you have from any other jobs on your 1040 form and will increase how much income tax you will pay.
In addition to that, you will probably need to pay Self-Employment tax, which is 15.3%* of your profit. This gets calculated on Schedule SE. There are minimum levels of profit you need to reach before you start to owe self-employment tax, so you need to look at the directions at tax time to figure out if you will owe it or not. If you truly only end up with $250 profit, you won't be paying any Self-Employment tax.
* Not exactly; see dave_thompson_085's comment for some details on this. As you can see, the math, thresholds, limits, and deductions can get a little complicated, so follow the instructions carefully, or better yet, get some tax software (or a paid professional) to help you out at tax time.