Currently, the fastest way would be to participate in events, assuming you have a good car that can earn all the position/timing rewards. For example, “the [day] heat” events help you get about 20-30 tokens.

Another good way is through R&D, Championships and EDD. All these all these are a profitable way to earn credits, with each mission completed getting you about 5-10 credits and some boss missions (AI) giving you up to 50.

You can also watch videos to earn tokens, 2 at a time. You can find individual videos in “token packs” in the shop, promotional video at bottom-left corner and one other place that I forgot. You can watch each of these 3 times, totalling 9 times thus 18 tokens.

Tokens can also be received in daily rewards, normally 5 tokens. These don't come across as much though.

You can also claim tokens in multiplayer, once you reach also certain numer of points. This requires a certain amount of dedication to multiplayer.

Last but not least, Mastery rewards sometimes comprise of tokens, but for the price of using credits to upgrade your car. E.g. mastery 10 of the Mercedes CLA 45 awards 250 tokens, and mastery 5 of Mazda RX8, 100 tokens. These give a tremendous amount of tokens but is a one-time reward.

Reference:
https://www.quora.com/What-are-the-best-ways-to-earn-tokens-for-free-in-Asphalt-8-Airborne