Learn English – Location of day of week in non-U.S. long format dates

The context that matters most is where you are located geographically (or which variety of English you otherwise wish to employ).

Paul covered the case of the US: "April 1, 2010". That would surely be understood in the UK too, but to my knowledge "1 April 2010" (NB: no comma) or "1/4/2010" would be more common there.

Edit: Based on some quick "research" I just did, most commonwealth countries (Australia, New Zealand, South Africa) also seem to prefer "1 April 2010", while in Canada "April 1, 2010" would be more common (probably due to US influence).

As Paul mentioned, YYYY-MM-DD is pretty good for getting across universally, yet concisely. In my opinion the format often used by airlines – "01 Apr 2010" – is useful too; there isn't much room for misinterpretation there.

When used in reference to time, date almost exclusively refers to a specific 24 hour period that begins at midnight and ends at 11:59pm. When used this way, the date will be specified with a year (CE or BCE), the name of the month, and the number of the day within that month. The day number is a positive whole number that may be used in ordinal form (first, second, third, etc.) The name of the weekday is rarely referenced when referring to a date.

When setting up an appointment, you typically use the term 'date' if the appointment is a long time away or in a formal business setting. When making appointments with friends, especially if they are happening within one week's time, you would use the term 'day'.

You ask a friend "What day do you want to have lunch?" The receptionist at your doctor's office will ask you "What date would you like to have your next appointment?"