You will probably want to use the standard mileage method instead. The standard mileage amount is around 55 cents per mile (changes from year to year) and includes allowances for fuel, maintenance (oil changes, tires, etc.) repairs, insurance and depreciation. It's easier to claim and usually more generous. To claim the standard mileage method, you need a record of your business miles from the app, a log book, or something similar, which must contain the date, the business purpose of the trip, and the mileage. Your miles from one drop off to the next pick up are also deductible even if the Uber app doesn't track them, but personal miles (like stopping at your favorite restaurant for lunch) are not deductible.
The alternative is the actual expense method. To use this method you need the same mileage records, plus you need your total miles for the year (personal plus business) so you can get the percentage of total miles that are business. Then you need all your expense records -- gas receipts, repairs and maintenance, insurance and depreciation. You claim a percentage of total expenses equal to the percentage of total miles that were for business. It's a lot more record keeping, and usually not as generous.
You can never deduct your car loan payment, although if you use the actual expense method you can deduct your lease payments.
You can add tolls and parking fees on top of whichever method you use.
Depreciation is either over 5 or 7 years (I'm too lazy to double check) and your basis for depreciation is not the purchase price, but the fair market value when you place it in service. (You don't have to limit or stop depreciation when it is included in the standard mileage method.) Which is another reason the standard method is usually more beneficial.
Finally, be aware that when you sell your vehicle, you may owe depreciation recapture for the depreciation you took, even though selling a used car is rarely a taxable event outside of business use of the vehicle.
