To claim medical miles, you need to keep a log of miles driven for medical purposes. This could be in any format, but a spreadsheet with the date, the itinerary and the distance driven and the reason would suffice.
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You can do a notebook in your car, or a spreadsheet, or something similar. What the IRS would want to see is the date, mileage driven, and purpose of the trip. The IRS will also want to know that the log was kept contemporaneously with the trips -- in other words, the log was written when the event was reasonably fresh in your mind and you weren't trying to fill it all out in December retroactive to January.
Since for medical expense deduction you can only deduct a flat 17¢ per mile, there's no point in writing down gas purchases.
You can, however, include road tolls and parking on top of the mileage, so make sure to note those as well.