The main source for gaining influence is spending money on the store and you get 10 influence for every dollar spent. Contributing to the community (creating videos, writing to the Wiki, making impressive fan art, etc.) should give you some influence too but so far that has been extremely rare. You can read more about influence on Wiki.
Guild and Villager tokens are for showing support for guilds and towns. You can buy and gift those to the leaders of guilds and towns and they will gain some benefits from them. Villager tokens increase the town population by 1, increase notoriety and after 3-5 tokens add a parcel of land to the town. Guild tokens increase notoriety, give research points or resources and for every 15 tokens the guild gets an additional building or an add-on for a building.