Tap the To-do List button on the left side of your screen to open a list of your current quests.
You can browse through different quests by tapping different quest icons to the left.
Each quest has a set of requirements that have to be met in order to complete it. Examples are: construct a certain building, collect profits from a business a certain number of times, collect and use certain items, etc.
Quests are very profitable in terms of money, goods and experience points. It is recommended to stick to them in order to advance through the game.
Some quests are timed, meaning that they should be ended before the time runs out.
Timed quests may usually be restarted if failed, but you will have to start the quest from the beginning, meaning that items that were already used will disappear.