Each day of an event, special entry points will appear across the city (e.g. Portals, Mechs, Mind Control, Anarchy). Reach them to start unique missions. There are no mission requirements and no event Energy. There are two types of Limited Rewards.
You can get up to four event Crates every time you complete a mission, depending on the number of mission Stars you achieve. An additional Progress Reward is unlocked once you get enough Stars by replaying missions. Once you claim the first Progress Reward, it will be replaced by the second one, and so on.
To start a City Event mission, you have to spend the special consumables -- that is, Batteries -- that you receive at the start of that same event, and on a daily basis. You can also purchase them in the Shop.