Jerry Lee
The "Entfernungspauschale" basically "commuting deduction" is 0,30€ per km distance from work, the airport. BOTH WAYS! This is ONLY the case for aircrews, unless it's one way. The maximum deduction you can get is 4700€ per year and you can either chose to get it in form of (1.) a tax return or (2.) in form of a "Freibetrag" basically a monthly tax exemption.
In case of (1.) you will need to maintain a "Fahrtenbuch". Basically a logbook (including gas receipts) of EVERY ride you make. No matter if private or work related.
In case of (2.) you can by showing your rosters prove that you will have around so and so many rides to the airport every month. Thereafter a tax exemption per month is put into your "Lohnsteuerkarte". This is the document that you (self employed) or your employer maintains to calculate your monthly/yearly tax payments.
You can also get a deduction on lease costs of your car. You then however have to prove that you are using your car to a certain extent just for work related purposes. I'm not sure, but I've heard something about 70%.