For Org mode to recognize timestamps, they need to be in the specific format. All commands listed below produce timestamps in the correct format.
Prompt for a date and insert a corresponding timestamp. When the cursor is at an existing timestamp in the buffer, the command is used to modify this timestamp instead of inserting a new one. When this command is used twice in succession, a time range is inserted. With a prefix, also add the current time.
Like C-c ., but insert an inactive timestamp that will not cause an agenda entry.
Change date at cursor by one day.
Change the item under the cursor in a timestamp. The cursor can be on a year, month, day, hour or minute. When the timestamp contains a time range like ‘15:30-16:30’, modifying the first time will also shift the second, shifting the time block with constant length. To change the length, modify the second time.
When Org mode prompts for a date/time, it will accept any string containing some date and/or time information, and intelligently interpret the string, deriving defaults for unspecified information from the current date and time. You can also select a date in the pop-up calendar. See the manual for more information on how exactly the date/time prompt works.