The most quickest way to generate gold quickly is through buying gold from the store. This is not recommended however as there are alternative methods to gaining gold effectively and at a much less cost. Grinding may be painful, but it is not worth wasting $10+ on something you can get in an hour.
Most Effective Method
The most effective method to gaining gold quickly is through the Multistage Airbase. While it may seem like a silly idea, there is actually a really simple way to win; the base has almost no armour. Launch at least 6 VLS Tomahawk missiles to destroy the base. You receive 8,000 gold per mission if it is three-starred. 6 tomahawk missiles are expensive (540,000 gold in total), but it is a good investment.
Warning: missiles can and do occasionally miss. For a more effective chance of hitting the base, carry more missiles.
Do the Montana mission:
Since it takes place in the fog, the battleship will never shoot you unless you are really close. Its inability to shoot at medium-long ranges make it an easy mission.
Do the Andrei-Pervozanny mission:
While not making a whole tonne of gold, this mission is easy for new players to complete. Rewarding you with 1,000 gold once completed.