what are the reaction mechanisms involved in the production of acid rain from atomospheric nitrogen?

Nitric oxide forms from nitrogen and oxygen at the high temperature in the engine.

Engine exhaust includes some NO.  NO reacts with oxygen and water vapor to make nitric acid.

During lightning some of the Nitrogen of atmosphere is converted into various type of Nitrogen oxides, because charge of lightning and very high temperature of spark provide it required reaction condition.
N2O5 + H2O -----> 2 HNO3
2NO2 + H2O ----> HNO3 + HNO2
N2O3 + H2O ---> 2 HNO2
 The major reason for acid rain is Nitrogen oxides of Fossil fuels. Most of the fossil fuels - Petroleum fuels contain some compound of nitrogen as they are formed from some living system of the past. When these fuels are used, Nitrogen containing compounds are oxidised to various forms of Nitrogen Oxides - usually represented as NOx at the high temperature in the engine or combustion system. These NOX form Nitric acid and Nitrous acid using moisture of atmosphere or water of rain drops.
There are many more complex reactions that uses few of other oxides like SOx, P2O5 and other things.