How to create a new event:
Tap on the start date or time to choose your start date:
Scroll up or down and select your desired date, or tap on the year (where it says 2015) to change the year.
Tapping on next or on the time at the top right hand corner brings you to the time picker. After selecting the hours it will automatically jump to the minute selector. If you want to go back just tap on the hour (in the screenshot this is the 9 in 9:30). If you prefer to use a 24 hour clock rather than AM and PM you can set this in up in preferences > date and time > time format.
Tap on the time zone (Central European Summer Time in the screenshot) to change the time zone of the start time. To change your default time zone, please do this via your phone's settings.
You can start typing a part of your location name and auto-suggestions will pop up.
Tapping on one of these will show you all the available time zones in that country.
Remember to repeat the steps for your event's end time if necessary. You can pick a different time zone for the event end time than the one chosen for the event start time if you'd like. This could be useful if you are given event details in another time zone but don't want to manually convert the times to your own time.
Here is the view event screen showing the event in your device time at the top, with the event start and end times in their chosen time zones below it.
In the future you'll probably also be able to set a custom home time zone to override the device time zone.
It's possible to use the old date and time pickers that were not combines. In that case, please enable either (or both) of the options in the preference menu. You'll need to tap on the date in the edit event screen to go to the date picker. Tapping on the time will lead you to the time picker.